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Journal articles on the topic 'Finite model theory'

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Published: 4 June 2021
Last updated: 26 January 2023

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1

Chatzidakis, Zoé. "Model theory of finite fields and pseudo-finite fields." Annals of Pure and Applied Logic 88, no. 2-3 (November 1997): 95–108. http://dx.doi.org/10.1016/s0168-0072(97)00017-1.

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2

Lotfallah, Wafik Boulos. "Strong convergence in finite model theory." Journal of Symbolic Logic 67, no. 3 (September 2002): 1083–92. http://dx.doi.org/10.2178/jsl/1190150151.

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AbstractIn [9] we introduced a new framework for asymptotic probabilities, in which a σ-additive measure is defined on the sample space of all sequences of finite models, where the universe of , is {1,2,…,n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in eventually almost surely or fails in eventually almost surely.In this paper we define the strong convergence law for formulas, which carries over the ideas of the strong 0-1 law to formulas with free variables, and roughly states that for each formula ϕ(x), the fraction of tuples a in , which satisfy the formula ϕ(x), almost surely has a limit as n tends to infinity.We show that the infinitary logic with finitely many variables has the strong convergence law for formulas for the uniform measure, and further characterize the measures on random graphs for which the strong convergence law holds.
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3

Fagin, Ronald. "Finite-model theory - a personal perspective." Theoretical Computer Science 116, no. 1 (August 1993): 3–31. http://dx.doi.org/10.1016/0304-3975(93)90218-i.

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4

Djordjević, Marko. "Finite variable logic, stability and finite models." Journal of Symbolic Logic 66, no. 2 (June 2001): 837–58. http://dx.doi.org/10.2307/2695048.

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We will study complete Ln-theories and their models, where Ln is the set of first order formulas in which at most n distinct variables occur. Here, by a complete Ln-theory we mean a theory such that for every Ln-sentence, it or its negation is implied by the theory. Hence, a complete Ln-theory need not necessarily be complete in the usual sense. Our approach is to transfer concepts and methods from stability theory, such as the order property and counting types, to the context of Ln-theories. So, in one sense, we will develop some rudimentary stability theory for a particular class of (possibly) incomplete theories. To make the ‘stability theoretic’ arguments work, we need to assume that models of the complete Ln-theory T which we consider can be amalgamated in certain ways. If this condition is satisfied and T has infinite models then there will exist models of T which are sufficiently saturated with respect to Ln. This allows us to use some counting types arguments from stability theory. If, moreover, we impose some finiteness conditions on the number of Ln-types and the length of Ln-definable orders then a sufficiently saturated model of T will be ω-categorical and ω-stable. Using the theory of ω-categorical and ω-stable structures we derive that T has arbitrarily large finite models.A different approach to combining stability theory with finite model theory is made by Hyttinen in [9] and [10].
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5

Dawar, Anuj. "FINITE MODEL THEORY (Perspectives in Mathematical Logic)." Bulletin of the London Mathematical Society 29, no. 4 (July 1997): 504–5. http://dx.doi.org/10.1112/s0024609396222416.

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6

Macpherson, Dugald. "Model theory of finite and pseudofinite groups." Archive for Mathematical Logic 57, no. 1-2 (September 19, 2017): 159–84. http://dx.doi.org/10.1007/s00153-017-0584-1.

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7

Alfaro, Jorge, Pablo González, and Ricardo Avila. "A finite quantum gravity field theory model." Classical and Quantum Gravity 28, no. 21 (October 12, 2011): 215020. http://dx.doi.org/10.1088/0264-9381/28/21/215020.

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8

Eberl, Matthias. "A Model Theory for the Potential Infinite." Reports on Mathematical Logic 57 (November 28, 2022): 3–30. http://dx.doi.org/10.4467/20842589rm.22.001.16658.

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We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely extensible finite. The main adoption is the interpretation of the universal quantifier, which has an implicit reection principle. Each universal quantification refers to an indefinitely large, but finite set. The quantified sets may increase, so after a reference by quantification, a further reference typically uses a larger, still finite set. We present the concepts for classical first-order logic and show that these dynamic models are sound and complete with respect to the usual inference rules. Moreover, a finite set of formulas requires a finite part of the increasing model for a correct interpretation.
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9

Rosen, Eric. "Some Aspects of Model Theory and Finite Structures." Bulletin of Symbolic Logic 8, no. 3 (September 2002): 380–403. http://dx.doi.org/10.2178/bsl/1182353894.

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Model theory is concerned mainly, although not exclusively, with infinite structures. In recent years, finite structures have risen to greater prominence, both within the context of mainstream model theory, e.g., in work of Lachlan, Cherlin, Hrushovski, and others, and with the advent of finite model theory, which incorporates elements of classical model theory, combinatorics, and complexity theory. The purpose of this survey is to provide an overview of what might be called the model theory of finite structures. Some topics in finite model theory have strong connections to theoretical computer science, especially descriptive complexity theory (see [26, 46]). In fact, it has been suggested that finite model theory really is, or should be, logic for computer science. These connections with computer science will, however, not be treated here.It is well-known that many classical results of ‘infinite model theory’ fail over the class of finite structures, including the compactness and completeness theorems, as well as many preservation and interpolation theorems (see [35, 26]). The failure of compactness in the finite, in particular, means that the standard proofs of many theorems are no longer valid in this context. At present, there is no known example of a classical theorem that remains true over finite structures, yet must be proved by substantially different methods. It is generally concluded that first-order logic is ‘badly behaved’ over finite structures.From the perspective of expressive power, first-order logic also behaves badly: it is both too weak and too strong. Too weak because many natural properties, such as the size of a structure being even or a graph being connected, cannot be defined by a single sentence. Too strong, because every class of finite structures with a finite signature can be defined by an infinite set of sentences. Even worse, every finite structure is defined up to isomorphism by a single sentence. In fact, it is perhaps because of this last point more than anything else that model theorists have not been very interested in finite structures. Modern model theory is concerned largely with complete first-order theories, which are completely trivial here.
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10

Lotfallah, Wafik Boulos. "Strong 0-1 laws in finite model theory." Journal of Symbolic Logic 65, no. 4 (December 2000): 1686–704. http://dx.doi.org/10.2307/2695069.

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AbstractWe introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequences A = {} of finite models, where the universe of is {1,2, …, n}. and use this framework to strengthen 0-1 laws for logics.
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11

Baldwin, J. "Finite and infinite model theory - a historical perspective." Logic Journal of IGPL 8, no. 5 (September 1, 2000): 605–28. http://dx.doi.org/10.1093/jigpal/8.5.605.

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12

Fuchs, Peter. "On pseudo-finite near-fields which have finite dimension over the centre." Proceedings of the Edinburgh Mathematical Society 32, no. 3 (October 1989): 371–75. http://dx.doi.org/10.1017/s0013091500004636.

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In [1] J. Ax studied a class of fields with similar properties as finite fields called pseudo-finite fields. One can prove that pseudo-finite fields are precisely the infinite models of the first-order theory of finite fields. Similarly a near-field F is called pseudo-finite if F is an infinite model of the first-order theory of finite near-fields. The structure theory of these near-fields has been initiated by U. Feigner in [5].
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13

Hella, Lauri, Phokion G. Kolaitis, and Kerkko Luosto. "Almost Everywhere Equivalence of Logics in Finite Model Theory." Bulletin of Symbolic Logic 2, no. 4 (December 1996): 422–43. http://dx.doi.org/10.2307/421173.

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AbstractWe introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L′ are two logics and μ is an asymptotic measure on finite structures, then L ≡a.e.L′ (μ) means that there is a class C of finite structures with μ(C) = 1 and such that L and L′ define the same queries on C. We carry out a systematic investigation of ≡a.e. with respect to the uniform measure and analyze the ≡a.e.-equivalence classes of several logics that have been studied extensively in finite model theory. Moreover, we explore connections with descriptive complexity theory and examine the status of certain classical results of model theory in the context of this new framework.
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14

Hausmann, Markus. "Symmetric spectra model global homotopy theory of finite groups." Algebraic & Geometric Topology 19, no. 3 (May 21, 2019): 1413–52. http://dx.doi.org/10.2140/agt.2019.19.1413.

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15

Papadopoulos, Loukas, and Ephrahim Garcia. "Probabilistic Finite Element Model Updating Using Random Variable Theory." AIAA Journal 39, no. 1 (January 2001): 193–95. http://dx.doi.org/10.2514/2.1292.

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16

Broersen, P. M., and H. E. Wensink. "On Finite Sample Theory for Autoregressive Model Order Selection." IEEE Transactions on Signal Processing 41, no. 1 (January 1993): 194. http://dx.doi.org/10.1109/tsp.1993.193138.

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17

Bologyubov, N. N., and V. N. Plechko. "Perturbation theory in the polaron model at finite temperature." Theoretical and Mathematical Physics 65, no. 3 (December 1985): 1255–63. http://dx.doi.org/10.1007/bf01036135.

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18

Pruschke, Th. "Perturbation theory of the Anderson model at finite U." Physica B: Condensed Matter 163, no. 1-3 (April 1990): 553–56. http://dx.doi.org/10.1016/0921-4526(90)90267-x.

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19

Papadopoulos, Loukas, and Ephrahim Garcia. "Probabilistic finite element model updating using random variable theory." AIAA Journal 39 (January 2001): 193–95. http://dx.doi.org/10.2514/3.14717.

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20

Compton, Kevin J. "Application of a Tauberian theorem to finite model theory." Archiv für Mathematische Logik und Grundlagenforschung 25, no. 1 (December 1985): 91–98. http://dx.doi.org/10.1007/bf02007559.

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21

Tsay Tzeng, S. Y., P. J. Ellis, T. T. S. Kuo, and E. Osnes. "Finite-temperature many-body theory with the Lipkin model." Nuclear Physics A 580, no. 2 (November 1994): 277–90. http://dx.doi.org/10.1016/0375-9474(94)90774-9.

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22

Grohe, Martin. "Finite Variable Logics in Descriptive Complexity Theory." Bulletin of Symbolic Logic 4, no. 4 (December 1998): 345–98. http://dx.doi.org/10.2307/420954.

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Throughout the development of finite model theory, the fragments of first-order logic with only finitely many variables have played a central role. This survey gives an introduction to the theory of finite variable logics and reports on recent progress in the area.For each k ≥ 1 we let Lk be the fragment of first-order logic consisting of all formulas with at most k (free or bound) variables. The logics Lk are the simplest finite-variable logics. Later, we are going to consider infinitary variants and extensions by so-called counting quantifiers.Finite variable logics have mostly been studied on finite structures. Like the whole area of finite model theory, they have interesting model theoretic, complexity theoretic, and combinatorial aspects. For finite structures, first-order logic is often too expressive, since each finite structure can be characterized up to isomorphism by a single first-order sentence, and each class of finite structures that is closed under isomorphism can be characterized by a first-order theory. The finite variable fragments seem to be promising candidates with the right balance between expressive power and weakness for a model theory of finite structures. This may have motivated Poizat [67] to collect some basic model theoretic properties of the Lk. Around the same time Immerman [45] showed that important complexity classes such as polynomial time (PTIME) or polynomial space (PSPACE) can be characterized as collections of all classes of (ordered) finite structures definable by uniform sequences of first-order formulas with a fixed number of variables and varying quantifier-depth.
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23

López-Picón, José Luis, Octavio Obregón, and José Ríos-Padilla. "A Proposal to Solve Finite N Matrix Theory: Reduced Model Related to Quantum Cosmology." Universe 8, no. 8 (August 11, 2022): 418. http://dx.doi.org/10.3390/universe8080418.

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The SU(N) invariant model of matrix theory that emerges as the regularization of the 11-dimensional super membrane is studied. This matrix model is identified with M theory in the limit N→∞. It has been conjectured that matrix models are also relevant for finite N where several examples and arguments have been given in the literature. By the use of a Dirac-like formulation usually developed in finding solutions in Supersymmetric Quantum Cosmology, we exhibit a method that could solve, in principle, any finite N model. As an example of our procedure, we choose a reduced SU(2) model and also show that this matrix model contains relevant supersymmetric quantum cosmological models as solutions. By these means, our solutions constitute an example in order to consider why the finite N matrix models are also relevant. Since the degrees of freedom of matrix models are, in some limit, identified with those of Super Yang Mills Theory SYM with a finite number of supercharges, our methodology offers the possibility, through some but yet unspecified identification, to relate the quantization presented here with that of SYM theory for any finite N.
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24

Bhattacharyya, Arun K. "An Accurate Model for Finite Array Patterns Based on Floquet Modal Theory." IEEE Transactions on Antennas and Propagation 63, no. 3 (March 2015): 1040–47. http://dx.doi.org/10.1109/tap.2015.2389249.

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25

AMENDOLA, GIOVANNI, NICOLA LEONE, and MARCO MANNA. "Finite model reasoning over existential rules." Theory and Practice of Logic Programming 17, no. 5-6 (August 24, 2017): 726–43. http://dx.doi.org/10.1017/s1471068417000369.

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AbstractOntology-based query answering asks whether a Boolean conjunctive query is satisfied by all models of a logical theory consisting of a relational database paired with an ontology. The introduction of existential rules (i.e., Datalog rules extended with existential quantifiers in rule heads) as a means to specify the ontology gave birth to Datalog+/-, a framework that has received increasing attention in the last decade, with focus also on decidability and finite controllability to support effective reasoning. Five basic decidable fragments have been singled out: linear, weakly acyclic, guarded, sticky, and shy. Moreover, for all these fragments, except shy, the important property of finite controllability has been proved, ensuring that a query is satisfied by all models of the theory iff it is satisfied by all its finite models. In this paper, we complete the picture by demonstrating that finite controllability of ontology-based query answering holds also for shy ontologies, and it therefore applies to all basic decidable Datalog+/- classes. To make the demonstration, we devise a general technique to facilitate the process of (dis)proving finite controllability of an arbitrary ontological fragment.
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26

SUZUKI, JUNJI, TARO NAGAO, and MIKI WADATI. "EXACTLY SOLVABLE MODELS AND FINITE SIZE CORRECTIONS." International Journal of Modern Physics B 06, no. 08 (April 20, 1992): 1119–80. http://dx.doi.org/10.1142/s021797929200058x.

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Recent developments in the theory of exactly solvable models are reviewed. Particular attention is paid to the finite size corrections to the Bethe ansatz equations. Baxter’s formula which relates a 2-dimensional statistical model with a 1-dimensional spin model is extended into the finite temperature case. A combination of this extension and the theory of finite size corrections gives a systematic method to evaluate low temperature expansions of physical quantities. Applications of the method to 1-dimensional quantum spin models are discussed. Throughout this paper, the usefulness of the soliton theory should be observed.
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27

Bozdog, D., and W. W. Olson. "An Advanced Shell Theory Based Tire Model." Tire Science and Technology 33, no. 4 (October 1, 2005): 227–38. http://dx.doi.org/10.2346/1.2174345.

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Abstract The objective of this paper is to investigate a class of general tire models that provides results suitable for usage in vehicle dynamics. Tire models currently used for vehicle dynamic analyses are overly simplistic (springs, a spring and damper combination or semi-elastic substance) or based on curve fits of experimental data. In contrast, the tire models used by major tire companies are extremely complex with solutions possible only by finite element analysis. Between these two extremes exists the potential for an elasticity based shell theory tire model. Micro-mechanics and composite laminate theories provide an integrated approach to the macroscopic behavior of the tire carcass and the tread support plies. This methodology has the capability of including centrifugal and friction forces. Finite difference methods are applied that produce reliable and accurate solutions of the tire response.
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28

Mignemi, S. "The Snyder Model and Quantum Field Theory." Ukrainian Journal of Physics 64, no. 11 (November 25, 2019): 991. http://dx.doi.org/10.15407/ujpe64.11.991.

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We review the main features of the relativistic Snyder model and its generalizations. We discuss the quantum field theory on this background using the standard formalism of noncommutative QFT and discuss the possibility of obtaining a finite theory.
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29

Song, Yooseob, and George Z. Voyiadjis. "Strain gradient finite element model for finite deformation theory: size effects and shear bands." Computational Mechanics 65, no. 5 (January 31, 2020): 1219–46. http://dx.doi.org/10.1007/s00466-020-01816-2.

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30

Schröder, Lutz. "A finite model construction for coalgebraic modal logic." Journal of Logic and Algebraic Programming 73, no. 1-2 (September 2007): 97–110. http://dx.doi.org/10.1016/j.jlap.2006.11.004.

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31

Krynicki, Michał, and Konrad Zdanowski. "Theories of arithmetics in finite models." Journal of Symbolic Logic 70, no. 1 (March 2005): 1–28. http://dx.doi.org/10.2178/jsl/1107298508.

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AbstractWe investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2–theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ1–theory of multiplication and order is decidable in finite models as well as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation.We consider also the spectrum problem. We show that the spectrum of arithmetic with multiplication and arithmetic with exponentiation is strictly contained in the spectrum of arithmetic with addition and multiplication.
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32

Moosa, Rahim, and Thomas Scanlon. "Model theory of fields with free operators in characteristic zero." Journal of Mathematical Logic 14, no. 02 (December 2014): 1450009. http://dx.doi.org/10.1142/s0219061314500093.

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Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme 𝒟 over a field A of characteristic zero, the theory of 𝒟-fields has a model companion 𝒟-CF0 which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types.
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33

ADLER, MARK, PIERRE VAN MOERBEKE, and DONG WANG. "RANDOM MATRIX MINOR PROCESSES RELATED TO PERCOLATION THEORY." Random Matrices: Theory and Applications 02, no. 04 (October 2013): 1350008. http://dx.doi.org/10.1142/s2010326313500081.

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This paper studies a number of matrix models of size n and the associated Markov chains for the eigenvalues of the models for consecutive n's. They are consecutive principal minors for two of the models, GUE with external source and the multiple Laguerre matrix model, and merely properly defined consecutive matrices for the third one, the Jacobi–Piñeiro model; nevertheless the eigenvalues of the consecutive models all interlace. We show: (i) For each of those finite models, we give the transition probability of the associated Markov chain and the joint distribution of the entire interlacing set of eigenvalues; we show this is a determinantal point process whose extended kernels share many common features. (ii) To each of these models and their set of eigenvalues, we associate a last-passage percolation model, either finite percolation or percolation along an infinite strip of finite width, yielding a precise relationship between the last-passage times and the eigenvalues. (iii) Finally, it is shown that for appropriate choices of exponential distribution on the percolation, with very small means, the rescaled last-passage times lead to the Pearcey process; this should connect the Pearcey statistics with random directed polymers.
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34

Wu, Heng Bin, and Ze Ping He. "The Finite Element Model of Discontinuous Rock Masses." Advanced Materials Research 243-249 (May 2011): 2948–51. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.2948.

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The traditional limit equilibrium theory could not consider the discontinuous property of rock slope, and the existing research methods for the discontinuous rock mass confined to the Discrete Element Method and Discontinuous Deformation Analysis. Based on the finite element theory, considering the strength reduction of the joint mechanical parameters, the slope stability with one or two sets joints are analyzed in this paper. The results show that, the sliding surface for one set joint slope is close to the joint dip, and the sliding surface for two sets joints slope is close to the control joint dip.
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35

Dixit, Narendra M., Piyush Srivastava, and Nisheeth K. Vishnoi. "A Finite Population Model of Molecular Evolution: Theory and Computation." Journal of Computational Biology 19, no. 10 (October 2012): 1176–202. http://dx.doi.org/10.1089/cmb.2012.0064.

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36

Trumper, Adolfo E., Luca Capriotti, and Sandro Sorella. "Finite-size spin-wave theory of the triangular Heisenberg model." Physical Review B 61, no. 17 (May 1, 2000): 11529–32. http://dx.doi.org/10.1103/physrevb.61.11529.

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37

HASHIGUCHI, Koichi. "Exact multiplicative finite strain theory based on subloading surface model." Proceedings of the Materials and Mechanics Conference 2016 (2016): GS—26. http://dx.doi.org/10.1299/jsmemm.2016.gs-26.

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38

S. P. Singh, R. P. Rudra, and W. T. Dickinson. "A Potential Theory-based Finite Element Model for Transient Recharge." Transactions of the ASAE 39, no. 5 (1996): 1879–89. http://dx.doi.org/10.13031/2013.27666.

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39

Voyiadjis, George Z., and Louay N. Mohammad. "Theory vs. experiment for finite strain viscoplastic, lagrangian constitutive model." International Journal of Plasticity 7, no. 4 (January 1991): 329–50. http://dx.doi.org/10.1016/0749-6419(91)90039-2.

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40

Hayashi, Masahito. "Asymptotic estimation theory for a finite-dimensional pure state model." Journal of Physics A: Mathematical and General 31, no. 20 (May 22, 1998): 4633–55. http://dx.doi.org/10.1088/0305-4470/31/20/006.

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41

Hayashi, M. "Asymptotic estimation theory for a finite-dimensional pure state model." Journal of Physics A: Mathematical and General 31, no. 41 (October 16, 1998): 8405. http://dx.doi.org/10.1088/0305-4470/31/41/015.

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42

YUROV, V. P., and AL B. ZAMOLODCHIKOV. "TRUNCATED COMFORMAL SPACE APPROACH TO SCALING LEE-YANG MODEL." International Journal of Modern Physics A 05, no. 16 (August 20, 1990): 3221–45. http://dx.doi.org/10.1142/s0217751x9000218x.

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A numerical approach to 2-D relativistic field theories is suggested. Considering a field theory model as an ultraviolet conformal field theory perturbed by a suitable relevant scalar operator one studies it in finite volume (on a circle). The perturbed Hamiltonian acts in the conformal field theory space of states and its matrix elements can be extracted from the conformal field theory. Truncation of the space at a reasonable level results in a finite dimensional problem for numerical analyses. The nonunitary field theory with the ultraviolet region controlled by the minimal conformal theory [Formula: see text] is studied in detail.
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43

VAN EIJCK, M. A., and CH G. VAN WEERT. "FINITE-TEMPERATURE RENORMALIZATION OF THE (ϕ4)4–MODEL." International Journal of Modern Physics B 10, no. 13n14 (June 30, 1996): 1485–97. http://dx.doi.org/10.1142/s0217979296000593.

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We summarize results of the finite-temperature renormalization group approach, formalized by Matsumoto, Nakano and Umezawa in 1984, for the λ(ϕ4)4-model. The flow parameter is the reference temperature at which the mass parameter and the coupling constant of the theory are defined through renormalization conditions. We derive flow equations to one-loop order, and integrate numerically from zero temperature to above the critical temperature. The mass and the coupling constant both vanish at the critical temperature, and are positive below and above the critical region. In the critical region dimensional reduction to an effective 3D theory takes place. The leading behavior of the mass at high temperature is linear with a small logarithmic sub-leading contribution.
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44

Mundici, Daniele. "Inverse topological systems and compactness in abstract model theory." Journal of Symbolic Logic 51, no. 3 (September 1986): 785–94. http://dx.doi.org/10.2307/2274032.

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AbstractGiven an abstract logic , generated by a set of quantifiers Qi, one can construct for each type τ a topological space Sτ, exactly as one constructs the Stone space for τ in first-order logic. Letting T be an arbitrary directed set of types, the set is an inverse topological system whose bonding mappings are naturally determined by the reduct operation on structures. We relate the compactness of to the topological properties of ST. For example, if I is countable then is compact iff for every τ each clopen subset of Sτ is of finite type and Sτ, is homeomorphic to limST, where T is the set of finite subtypes of τ. We finally apply our results to concrete logics.
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45

Barbina, Silvia, and Enrique Casanovas. "Model theory of Steiner triple systems." Journal of Mathematical Logic 20, no. 02 (December 31, 2019): 2050010. http://dx.doi.org/10.1142/s0219061320500105.

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A Steiner triple system (STS) is a set [Formula: see text] together with a collection [Formula: see text] of subsets of [Formula: see text] of size 3 such that any two elements of [Formula: see text] belong to exactly one element of [Formula: see text]. It is well known that the class of finite STS has a Fraïssé limit [Formula: see text]. Here, we show that the theory [Formula: see text] of [Formula: see text] is the model completion of the theory of STSs. We also prove that [Formula: see text] is not small and it has quantifier elimination, [Formula: see text], [Formula: see text], elimination of hyperimaginaries and weak elimination of imaginaries.
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46

Magnitsky, I. V., F. R. Odinabekov, and E. S. Sergeeva. "The Development of Multi-Directional Spatially Reinforced Material Structural Theory." Solid State Phenomena 284 (October 2018): 146–51. http://dx.doi.org/10.4028/www.scientific.net/ssp.284.146.

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Finite-element simulation of the spatially reinforced composite material elastic properties is performed. The simulation models are built in two steps: first, a 4DL-reinforced material model simulating a perfect matrix/rod contact is built; second, an improved simulation model is developed, taking into account the possibility of separation between the composite components. Comparison is made between the results obtained numerically and those based on the existing analytical models. With these finite-element simulation models, it is possible to estimate the required composite elastic properties to be used when designing structural components based on those materials.
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47

TIERZ, MIGUEL. "CHERN–SIMONS THEORY, EXACTLY SOLVABLE MODELS AND FREE FERMIONS AT FINITE TEMPERATURE." Modern Physics Letters A 24, no. 39 (December 21, 2009): 3157–71. http://dx.doi.org/10.1142/s0217732309032071.

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We show that matrix models in Chern–Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian model and the Calogero model. We compute the corresponding Hamiltonians, ground-state wave functions and ground-state energies and point out that the models can be interpreted as quasi-1D Coulomb plasmas. We also study the relationship between Chern–Simons theory on S3 and a system of N one-dimensional fermions at finite temperature with harmonic confinement. In particular, we show that the Chern–Simons partition function can be described by the density matrix of the free fermions in a very particular, crystalline, configuration. For this, we both use the Brownian motion and the matrix model description of Chern–Simons theory and find several common features with c = 1 theory at finite temperature. Finally, using the exactly solvable model result, we show that the finite temperature effect can be described with a specific two-body interaction term in the Hamiltonian, with 1D Coulombic behavior at large separations.
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48

Liu, Yang, Zhong Dong Duan, and Hui Li. "Updating of Finite Element Model in Considering Mode Errors with Fuzzy Theory." Key Engineering Materials 413-414 (June 2009): 785–92. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.785.

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Finite element model updating aims at reconciling the analytical model with the test one, to acquire a refined model with high-fidelity in structural dynamic properties. However, testing data are inevitable polluted by noises. In this study, the mode parameters and design variables are modeled as fuzzy variables, and a fuzzy model updating method is developed. Instead of a single optimal model, a set of satisfactory models is obtained. The most physically compatible solution is sorted by insights to the structures. The proposed method is applied to a real concrete bridge, for which a physically meaningful model is identified.
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49

Semukhin, Pavel. "Prime models of finite computable dimension." Journal of Symbolic Logic 74, no. 1 (March 2009): 336–48. http://dx.doi.org/10.2178/jsl/1231082315.

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AbstractWe study the following open question in computable model theory: does there exist a structure of computable dimension two which is the prime model of its first-order theory? We construct an example of such a structure by coding a certain family of c.e. sets with exactly two one-to-one computable enumerations into a directed graph. We also show that there are examples of such structures in the classes of undirected graphs, partial orders, lattices, and integral domains.
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50

Hodkinson, Ian, and Martin Otto. "Finite Conformal Hypergraph Covers and Gaifman Cliques in Finite Structures." Bulletin of Symbolic Logic 9, no. 3 (September 2003): 387–405. http://dx.doi.org/10.2178/bsl/1058448678.

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AbstractWe provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques—thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF.
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