Finite Structures With Few Types

Author : Gregory L. Cherlin
Publisher : Princeton University Press
ISBN 13 : 0691113327
Total Pages : 201 pages
Book Rating : 4.26/5 ( download)

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Download or read book Finite Structures with Few Types written by Gregory L. Cherlin and published by Princeton University Press. This book was released on 2003 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics. The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries). The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.

Author : Gregory L. Cherlin
Publisher : Princeton University Press
ISBN 13 : 9780691113319
Total Pages : 204 pages
Book Rating : 4.19/5 ( download)

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Download or read book Finite Structures with Few Types written by Gregory L. Cherlin and published by Princeton University Press. This book was released on 2003 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics. The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries). The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.

Author : Norbert W Sauer
Publisher : Springer Science & Business Media
ISBN 13 : 9401120803
Total Pages : 452 pages
Book Rating : 4.07/5 ( download)

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Download or read book Finite and Infinite Combinatorics in Sets and Logic written by Norbert W Sauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.

Author : Javier Esparza
Publisher : Cambridge University Press
ISBN 13 : 0521718201
Total Pages : 355 pages
Book Rating : 4.02/5 ( download)

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Download or read book Finite and Algorithmic Model Theory written by Javier Esparza and published by Cambridge University Press. This book was released on 2011-03-10 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.

Author : Bradd T. Hart
Publisher : Springer Science & Business Media
ISBN 13 : 9401589232
Total Pages : 285 pages
Book Rating : 4.39/5 ( download)

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Download or read book Algebraic Model Theory written by Bradd T. Hart and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

Author : S. Barry Cooper
Publisher : Cambridge University Press
ISBN 13 : 0521635500
Total Pages : 433 pages
Book Rating : 4.09/5 ( download)

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Download or read book Models and Computability written by S. Barry Cooper and published by Cambridge University Press. This book was released on 1999-06-17 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second of two volumes providing a comprehensive guide to the current state of mathematical logic.

Author : Lutz Strungmann
Publisher : American Mathematical Soc.
ISBN 13 : 082186923X
Total Pages : 336 pages
Book Rating : 4.39/5 ( download)

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Download or read book Groups and Model Theory written by Lutz Strungmann and published by American Mathematical Soc.. This book was released on 2012 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the conference Groups and Model Theory, held 2011, in Ruhr, Germany. Articles cover abelian groups, modules over commutative rings, permutation groups, automorphism groups of homogeneous structures such as graphs, relational structures, geometries, topological spaces or groups, consequences of model theoretic properties like stability or categoricity, subgroups of small index, the automorphism tower problem, as well as random constructions.

Author : David M. Evans
Publisher : Cambridge University Press
ISBN 13 : 052158955X
Total Pages : 232 pages
Book Rating : 4.50/5 ( download)

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Download or read book Model Theory of Groups and Automorphism Groups written by David M. Evans and published by Cambridge University Press. This book was released on 1997-07-10 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys recent interactions between model theory and other branches of mathematics, notably group theory.

Author : Gena Hahn
Publisher : Springer Science & Business Media
ISBN 13 : 9401589372
Total Pages : 434 pages
Book Rating : 4.76/5 ( download)

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Download or read book Graph Symmetry written by Gena Hahn and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

Author : R.L. Graham
Publisher : Elsevier
ISBN 13 : 008093384X
Total Pages : 2404 pages
Book Rating : 4.49/5 ( download)

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Download or read book Handbook of Combinatorics written by R.L. Graham and published by Elsevier. This book was released on 1995-12-11 with total page 2404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Combinatorics