Lectures on Infinitary Model Theory

Author: David Marker

Publisher: Cambridge University Press

ISBN: 1107181933

Category: Mathematics

Page: 192

View: 8029

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Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
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Sets, Models and Proofs

Author: Ieke Moerdijk,Jaap van Oosten

Publisher: Springer

ISBN: 3319924141

Category: Mathematics

Page: 141

View: 9945

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This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
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Model Theory and the Philosophy of Mathematical Practice

Formalization without Foundationalism

Author: John T. Baldwin

Publisher: Cambridge University Press

ISBN: 1108103014

Category: Science

Page: 352

View: 7666

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Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics.
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Logic Colloquium '02

Lecture Notes in Logic 27

Author: Zoé Chatzidakis,Peter Koepke,Wolfram Pohlers

Publisher: A K Peters/CRC Press

ISBN: N.A

Category: Mathematics

Page: 359

View: 3009

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This book is a compilation of papers presented at the 2002 European Summer Meeting of the Association for Symbolic Logic and the associated Colloquium Logicum 2002 conference. It includes tutorials and research articles from some of the world's preeminent logicians. Topics presented span all areas of mathematical logic, with a particular emphasis on Computability Theory and Proof Theory.
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