A Course in Model Theory: The Fine Structure of N1-Categorical Theories PDF Download
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Author: Katrin Tent
Publisher:
ISBN: 9781139228985
Category : Model theory
Languages : en
Pages : 248
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Book Description
This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.
Author: Katrin Tent
Publisher:
ISBN: 9781139228985
Category : Model theory
Languages : en
Pages : 248
Get Book Here
Book Description
This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.
Author: Katrin Tent
Publisher: Cambridge University Press
ISBN: 052176324X
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Concise introduction to current topics in model theory, including simple and stable theories.
Author: Gerald E Sacks
Publisher: World Scientific Publishing Company
ISBN: 9813107324
Category : Mathematics
Languages : en
Pages : 220
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Book Description
This book contains the material for a first course in pure model theory with applications to differentially closed fields. Topics covered in this book include saturated model criteria for model completeness and elimination of quantifiers; Morley rank and degree of element types; categoricity in power; two-cardinal theorems; existence and uniqueness of prime model extensions of substructures of models of totally transcendental theories; and homogeneity of models of ϖ1-categorical theories.
Author: Michael Makkai
Publisher: American Mathematical Soc.
ISBN: 9780821854372
Category : Mathematics
Languages : en
Pages : 188
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Book Description
Author: M. Makkai
Publisher: Springer
ISBN: 3540371001
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Author: Pierre Simon
Publisher: Cambridge University Press
ISBN: 1107057752
Category : Mathematics
Languages : en
Pages : 165
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Book Description
The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
Author: Daniel S. Freed
Publisher: American Mathematical Soc.
ISBN: 1470452065
Category : Algebraic topology
Languages : en
Pages : 186
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Book Description
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Author: Neil Dewar
Publisher: Cambridge University Press
ISBN: 1108910467
Category : Philosophy
Languages : en
Pages : 82
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Book Description
This Element explores what it means for two theories in physics to be equivalent (or inequivalent), and what lessons can be drawn about their structure as a result. It does so through a twofold approach. On the one hand, it provides a synoptic overview of the logical tools that have been employed in recent philosophy of physics to explore these topics: definition, translation, Ramsey sentences, and category theory. On the other, it provides a detailed case study of how these ideas may be applied to understand the dynamical and spatiotemporal structure of Newtonian mechanics - in particular, in light of the symmetries of Newtonian theory. In so doing, it brings together a great deal of exciting recent work in the literature, and is sure to be a valuable companion for all those interested in these topics.
Author: John T. Baldwin
Publisher: American Mathematical Soc.
ISBN: 0821848933
Category : Mathematics
Languages : en
Pages : 251
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Book Description
"Modern model theory began with Morley's categoricity theorem: A countable first-order theory that has a unique (up to isomorphism) model in one uncountable cardinal (i.e., is categorical in cardinality) if and only if the same holds in all uncountable cardinals. Over the last 35 years Shelah made great strides in extending this result to infinitary logic, where the basic tool of compactness fails. He invented the notion of an Abstract Elementary Class to give a unifying semantic account of theories in first-order, infinitary logic and with some generalized quantifiers. Zilber developed similar techniques of infinitary model theory to study complex exponentiation." "This book provides the first unified and systematic exposition of this work. The many examples stretch from pure model theory to module theory and covers of Abelian varieties. Assuming only a first course in model theory, the book expounds eventual categoricity results (for classes with amalgamation) and categoricity in excellent classes. Such crucial tools as Ehrenfeucht-Mostowski models, Galois types, tameness, omitting-types theorems, multi-dimensional amalgamation, atomic types, good sets, weak diamonds, and excellent classes are developed completely and methodically. The (occasional) reliance on extensions of basic set theory is clearly laid out. The book concludes with a set of open problems." --Book Jacket.
Author: Antonio Montalbán
Publisher: Cambridge University Press
ISBN: 1108534422
Category : Mathematics
Languages : en
Pages : 214
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Book Description
In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.
