Relevant bibliographies by topics / Mathematical Logic, Set Theory, Lattices and Combinatorics

Academic literature on the topic 'Mathematical Logic, Set Theory, Lattices and Combinatorics'

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Published: 4 June 2021
Last updated: 1 February 2022

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Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Mathematical Logic, Set Theory, Lattices and Combinatorics.'

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Journal articles on the topic "Mathematical Logic, Set Theory, Lattices and Combinatorics"

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Mileti, Joseph R. "Partition Theorems and Computability Theory." Bulletin of Symbolic Logic 11, no. 3 (September 2005): 411–27. http://dx.doi.org/10.2178/bsl/1122038995.

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The connections between mathematical logic and combinatorics have a rich history. This paper focuses on one aspect of this relationship: understanding the strength, measured using the tools of computability theory and reverse mathematics, of various partition theorems. To set the stage, recall two of the most fundamental combinatorial principles, König's Lemma and Ramsey's Theorem. We denote the set of natural numbers by ω and the set of finite sequences of natural numbers by ω<ω. We also identify each n ∈ ω with its set of predecessors, so n = {0, 1, 2, …, n − 1}.
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WEINERT, THILO. "William Chan, An introduction to combinatorics of determinacy, Trends in Set Theory (S. Coskey and G. Sargsyan, editors), Contemporary Mathematics, vol. 752, Providence, RI, American Mathematical Society, 2020, pp. 21–75." Bulletin of Symbolic Logic 27, no. 1 (March 2021): 91–93. http://dx.doi.org/10.1017/bsl.2020.37.

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Lubarsky, Robert. "Patrick Farrington. Hinges and automorphisms of the degrees of non-constructibility. The journal of the London Mathematical Society, ser. 2 vol. 28 (1983), pp. 193–202. - Petr Hájek. Some results on degrees of constructibility. Higher set theory, Proceedings, Oberwolfach, Germany, April 13–23, 1977, edited by G. H. Müller and D. S. Scott, Lecture notes in mathematics, vol. 669, Springer-Verlag, Berlin, Heidelberg, and New York, 1978, pp. 55–71. - Zofia Adamowicz. On finite lattices of degrees of constructibility of reals. The journal of symbolic logic, vol. 41 (1976), pp. 313–322. - Zofia Adamowicz. Constructive semi-lattices of degrees of constructibility. Set theory and hierarchy theory V, Bierutowice, Poland 1976, edited by A. Lachlan, M. Srebrny, and A. Zarach, Lecture notes in mathematics, vol. 619, Springer-Verlag, Berlin, Heidelberg, and New York, 1977, pp. 1–43." Journal of Symbolic Logic 54, no. 3 (September 1989): 1109–11. http://dx.doi.org/10.2307/2274781.

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Eklof, Paul C. "Fred Appenzeller. An independence result in quadratic form theory: infinitary combinatorics applied to ε-Hermitian spaces. The journal of symbolic logic, vol. 54 (1989), pp. 689–699. - Otmar Spinas. Linear topologies on sesquilinear spaces of uncountable dimension. Fundamenta mathematicae, vol. 139 (1991), pp. 119–132. - James E. Baumgartner, Matthew Foreman, and Otmar Spinas. The spectrum of the Γ-invariant of a bilinear space. Journal of algebra, vol. 189 (1997), pp. 406–418. - James E. Baumgartner and Otmar Spinas. Independence and consistency proofs in quadratic form theory. The journal of symbolic logic, vol. 56 (1991), pp. 1195–1211. - Otmar Spinas. Iterated forcing in quadratic form theory. Israel journal of mathematics, vol. 79 (1992), pp. 297–315. - Otmar Spinas. Cardinal invariants and quadratic forms. Set theory of the reals, edited by Haim Judah, Israel mathematical conference proceedings, vol. 6, Gelbart Research Institute for Mathematical Sciences, Bar-Ilan University, Ramat-Gan 1993, distributed by the American Mathematical Society, Providence, pp. 563–581. - Saharon Shelah and Otmar Spinas. Gross spaces. Transactions of the American Mathematical Society, vol. 348 (1996), pp. 4257–4277." Bulletin of Symbolic Logic 7, no. 2 (June 2001): 285–86. http://dx.doi.org/10.2307/2687785.

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Dissertations / Theses on the topic "Mathematical Logic, Set Theory, Lattices and Combinatorics"

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Vu, Xuan. "Analysis of necessary conditions for the optimal control of a train." 2006. http://arrow.unisa.edu.au:8081/1959.8/45958.

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The scheduling and Control Group at the University of South Australia has been studying the optimal control of trains for many years, and has developed in-cab devices that help drivers stay on time and minimise energy use. In this thesis, we re-examine the optimal control theory for the train control problem. In particular, we study the optimal control around steep sections of track. To calculate an optimal driving strategy we need a realistic model of train performance. In particular, we need to know a coefficient of rolling resistance and a coefficient of aerodynamic drag. In practice, these coefficients are different for every train and difficult to predict. In the thesis, we study the use of mathematical filters to estimate model parameters from observations of actual train performance.
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(11205846), Pablo J. Andujar Guerrero. "DEFINABLE TOPOLOGICAL SPACES IN O-MINIMAL STRUCTURES." Thesis, 2021.

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We further the research in o-minimal topology by studying in full generality definable topological spaces in o-minimal structures. These are topological spaces $(X, \tau)$, where $X$ is a definable set in an o-minimal structure and the topology $\tau$ has a basis that is (uniformly) definable. Examples include the canonical o-minimal "euclidean" topology, “definable spaces” in the sense of van den Dries [17], definable metric spaces [49], as well as generalizations of classical non-metrizable topological spaces such as the Split Interval and the Alexandrov Double Circle.

We develop a usable topological framework in our setting by introducing definable analogues of classical topological properties such as separability, compactness and metrizability. We characterize these notions, showing in particular that, whenever the underlying o-minimal structure expands $(\mathbb{R},<)$, definable separability and compactness are equivalent to their classical counterparts, and a similar weaker result for definable metrizability. We prove the equivalence of definable compactness and various other properties in terms of definable curves and types. We show that definable topological spaces in o-minimal expansions of ordered groups and fields have properties akin to first countability. Along the way we study o-minimal definable directed sets and types. We prove a density result for o-minimal types, and provide an elementary proof within o-minimality of a statement related to the known connection between dividing and definable types in o-minimal theories.

We prove classification and universality results for one-dimensional definable topological spaces, showing that these can be largely described in terms of a few canonical examples. We derive in particular that the three element basis conjecture of Gruenhage [25] holds for all infinite Hausdorff definable topological spaces in o-minimal structures expanding $(\mathbb{R},<)$, i.e. any such space has a definable copy of an interval with the euclidean, discrete or lower limit topology.

A definable topological space is affine if it is definably homeomorphic to a euclidean space. We prove affineness results in o-minimal expansions of ordered fields. This includes a result for Hausdorff one-dimensional definable topological spaces. We give two new proofs of an affineness theorem of Walsberg [49] for definable metric spaces. We also prove an affineness result for definable topological spaces of any dimension that are Tychonoff in a definable
sense, and derive that a large class of locally affine definable topological spaces are affine.
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(11008509), Nathanael D. Cox. "Two Problems in Applied Topology." Thesis, 2021.

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In this thesis, we present two main results in applied topology.
In our first result, we describe an algorithm for computing a semi-algebraic description of the quotient map of a proper semi-algebraic equivalence relation given as input. The complexity of the algorithm is doubly exponential in terms of the size of the polynomials describing the semi-algebraic set and equivalence relation.
In our second result, we use the fact that homology groups of a simplicial complex are isomorphic to the space of harmonic chains of that complex to obtain a representative cycle for each homology class. We then establish stability results on the harmonic chain groups.
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Books on the topic "Mathematical Logic, Set Theory, Lattices and Combinatorics"

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NATO Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic (1991 Banff, Alta.). Finite and infinite combinatorics in sets and logic: [proceedings of the NATO Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic, Banff, Alberta, Canada, April 21-May 4, 1991]. Dordrecht: Kluwer Academic Publishers, 1993.

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Chartrand, Gary. Mathematical proofs: A transition to advanced mathematics. 2nd ed. Boston: Pearson/Addison Wesley, 2008.

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Gerhard, Gierz, ed. Continuous lattices and domains. Cambridge, U.K: Cambridge University Press, 2003.

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Lawson, J. D., M. Mislove, G. Gierz, K. H. Hofmann, K. Keimel, and D. S. Scott. Continuous Lattices and Domains (Encyclopedia of Mathematics and its Applications). Cambridge University Press, 2003.

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(Editor), N. W. Sauer, R. E. Woodrow (Editor), and B. Sands (Editor), eds. Finite and Infinite Combinatorics in Sets and Logic (NATO Science Series C: (closed)). Springer, 1993.

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Mathematical Proofs: A Transition to Advanced Mathematics. Pearson Education, Limited, 2007.

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Mathematical Proofs: A Transition to Advanced Mathematics. Pearson, 2018.

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Polimeni, Albert D., Zhang Ping, and Gary Chartrand. Mathematical Proofs: A Transition to Advanced Mathematics. Addison Wesley, 2002.

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Polimeni, Albert D., Ping Zhang, and Gary Chartrand. Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition). 2nd ed. Addison Wesley, 2007.

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Mathematical Proofs : A Transition to Advanced Mathematics: International Edition. Pearson Education, Limited, 2012.

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