Classification of countable models of complete theories. Рart 2 PDF Download
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Author: Sergey Sudoplatov
Publisher: Litres
ISBN: 5041454795
Category : Mathematics
Languages : en
Pages : 394
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Book Description
The book is the second part of the monograph “Classification of countable models of complete theories” consisting of two parts. In the book, generic Ehrenfeucht theories and realizations of Rudin–Keisler preorders are considered as well as a solution of the Goncharov–Millar problem on the existence of Ehrenfeucht theories with countable models which are not almost homogeneous, stable Ehrenfeucht theories solving the Lachlan problem, hypergraphs of prime models, distributions of countable models of small theories, and distributions of countable models of theories with continuum many types.The book is intended for specialists interested in Mathematical Logic.
Author: Sergey Sudoplatov
Publisher: Litres
ISBN: 5041454795
Category : Mathematics
Languages : en
Pages : 394
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Book Description
The book is the second part of the monograph “Classification of countable models of complete theories” consisting of two parts. In the book, generic Ehrenfeucht theories and realizations of Rudin–Keisler preorders are considered as well as a solution of the Goncharov–Millar problem on the existence of Ehrenfeucht theories with countable models which are not almost homogeneous, stable Ehrenfeucht theories solving the Lachlan problem, hypergraphs of prime models, distributions of countable models of small theories, and distributions of countable models of theories with continuum many types.The book is intended for specialists interested in Mathematical Logic.
Author: Boris Zilber
Publisher: American Mathematical Soc.
ISBN: 9780821897454
Category : Mathematics
Languages : en
Pages : 132
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Book Description
The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.
Author: John T. Baldwin
Publisher: Springer
ISBN: 3540480498
Category : Mathematics
Languages : en
Pages : 512
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Book Description
Author: Wilfrid Hodges
Publisher: Cambridge University Press
ISBN: 9780521587136
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
Author: Mike Prest
Publisher: Cambridge University Press
ISBN: 0521348331
Category : Mathematics
Languages : en
Pages : 402
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Book Description
In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first time.
Author: Saharon Shelah
Publisher: Springer
ISBN: 3540397884
Category : Mathematics
Languages : en
Pages : 289
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Book Description
Author: S. Shelah
Publisher: Elsevier
ISBN: 008088024X
Category : Computers
Languages : en
Pages : 741
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Book Description
In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text. The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m
Author: Bradd T. Hart
Publisher: Springer Science & Business Media
ISBN: 9401589232
Category : Mathematics
Languages : en
Pages : 285
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Book Description
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: Ali Enayat
Publisher: American Mathematical Soc.
ISBN: 0821835351
Category : Mathematics
Languages : en
Pages : 184
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Book Description
This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.
Author: Sy-David Friedman
Publisher: American Mathematical Soc.
ISBN: 0821894757
Category : Mathematics
Languages : en
Pages : 92
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Book Description
Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.
