Relevant bibliographies by topics / Stability theory[Forking theory]

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Academic literature on the topic 'Stability theory[Forking theory]'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Stability theory[Forking theory]"

1

Kim, Byunghan. "Simplicity, and stability in there." Journal of Symbolic Logic 66, no. 2 (2001): 822–36. http://dx.doi.org/10.2307/2695047.

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AbstractFirstly, in this paper, we prove that the equivalence of simplicity and the symmetry of forking. Secondly, we attempt to recover definability part of stability theory to simplicity theory. In particular, using elimination of hyperimaginaries we prove that for any supersimple T. canonical base of an amalgamation class is the union of names of ψ-definitions of , ψ ranging over stationary L-formulas in . Also, we prove that the same is true with stable formulas for an 1-based theory having elimination of hyperimaginaries. For such a theory, the stable forking property holds, too.
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2

Ng, Siu-Ah. "A generalization of forking." Journal of Symbolic Logic 56, no. 3 (1991): 813–22. http://dx.doi.org/10.2178/jsl/1183743730.

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Given a subset A of a fixed saturated model , we let denote the algebra of definable subsets of the domain of M of with parameters from A. Then a complete type p over A can be regarded as a measure on , assigning the value 1 to members of p and 0 to nonmembers. In [5] and [6], Keisler developed a theory of forking concerning probability measures. Therefore it generalizes the ordinary theory. On a different track, we can view the complement of the type p, or the collection of null sets of any measure on , as ideals on . Moreover, ideals and the pseudometric of a measure form examples of the so-
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3

ARGOTY, CAMILO. "FORKING AND STABILITY IN THE REPRESENTATIONS OF A C*-ALGEBRA." Journal of Symbolic Logic 80, no. 3 (2015): 785–96. http://dx.doi.org/10.1017/jsl.2015.23.

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AbstractWe show that the theory of a nondegenerate representation of a C*-algebra ${\cal A}$ over a Hilbert space H is superstable. Also, we characterize forking, orthogonality and domination of types.
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4

Hart, Bradd, Byunghan Kim, and Anand Pillay. "Coordinatisation and canonical bases in simple theories." Journal of Symbolic Logic 65, no. 1 (2000): 293–309. http://dx.doi.org/10.2307/2586538.

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In this paper we discuss several generalization of theorems from stability theory to simple theories. Cherlin and Hrushovski, in [2] develop a substitute for canonical bases in finite rank, ω-categorical supersimple theories. Motivated by methods there, we prove the existence of canonical bases (in a suitable sense) for types in any simple theory. This is done in Section 2. In general these canonical bases will (as far as we know) exist only as “hyperimaginaries”, namely objects of the form a/E where a is a possibly infinite tuple and E a type-definable equivalence relation. (In the supersimpl
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5

d’Elbée, Christian. "Expansions and Neostability in Model Theory." Bulletin of Symbolic Logic 27, no. 2 (2021): 216–17. http://dx.doi.org/10.1017/bsl.2021.26.

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AbstractThis thesis is concerned with the expansions of algebraic structures and their fit in Shelah’s classification landscape.The first part deals with the expansion of a theory by a random predicate for a substructure model of a reduct of the theory. Let T be a theory in a language $\mathcal {L}$ . Let $T_0$ be a reduct of T. Let $\mathcal {L}_S = \mathcal {L}\cup \{S\}$ , for S a new unary predicate symbol, and $T_S$ be the $\mathcal {L}_S$ -theory that axiomatises the following structures: $(\mathscr {M},\mathscr {M}_0)$ consist of a model $\mathscr {M}$ of T and S is a predicate for a mo
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6

Ben-Yaacov, Itay, Ivan Tomašić, and Frank O. Wagner. "The Group Configuration in Simple Theories and its Applications." Bulletin of Symbolic Logic 8, no. 2 (2002): 283–98. http://dx.doi.org/10.2178/bsl/1182353874.

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AbstractIn recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or, in the ω-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity.The proof necessitated an extension of the model-theoretic framework to include almost hyperimaginaries, and the study of polygroups.
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7

García, Darío, Dugald Macpherson, and Charles Steinhorn. "Pseudofinite structures and simplicity." Journal of Mathematical Logic 15, no. 01 (2015): 1550002. http://dx.doi.org/10.1142/s0219061315500026.

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We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are made to produc
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8

Tsuboi, Akito. "On the number of independent partitions." Journal of Symbolic Logic 50, no. 3 (1985): 809–14. http://dx.doi.org/10.2307/2274333.

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In [3], Shelah defined the cardinals κn(T) and , for each theory T and n < ω. κn(T) is the least cardinal κ without a sequence (pi)i<κ of complete n-types such that pi is a forking extension of pj for all i < j < κ. It is essential in computing the stability spectrum of a stable theory. On the other hand is called the number of independent partitions of T. (See Definition 1.2 below.) Unfortunately this invariant has not been investigated deeply. In the author's opinion, this unfortunate situation of is partially due to the fact that its definition is complicated in expression. In t
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9

Iovino, José. "On the maximality of logics with approximations." Journal of Symbolic Logic 66, no. 4 (2001): 1909–18. http://dx.doi.org/10.2307/2694984.

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In this paper we analyze some aspects of the question of using methods from model theory to study structures of functional analysis.By a well known result of P. Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem). However, one may consider extending the scope of first order in a different sense, specifically, by expanding the class of structures that are regarded as models (e.g., including Banach algebras or other structures of functional analysis), and
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10

Zhang, Xue Peng. "Stability Bearing Capacity of Concrete Filled Thin-Walled Circular Steel Tubular Column under Axial Compression." Advanced Materials Research 690-693 (May 2013): 720–23. http://dx.doi.org/10.4028/www.scientific.net/amr.690-693.720.

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The bearing capacity formula of concrete filled thin-walled steel tubular (CFTST) short column was established based on limit equilibrium method, and the reasonable value fork1in Richart Strength Model was regression introduced adapted with concrete stress-strain relations. According to the elasticity modulus theory, the calculation formulas of stability bearing capacity of CFTST slender column were deduced, reasonable considering the interactions between steel tube and concrete. And the calculation process is relatively simple which avoiding complicated iterations used in the conventional cal
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