Classification Of Countable Models Of Complete Theories Art 1 PDF Download
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| Author | : Sergey Sudoplatov |
| Publisher | : Litres |
| Total Pages | : 326 |
| Release | : 2022-01-29 |
| Genre | : Mathematics |
| ISBN | : 5041454787 |
Download Classification of countable models of complete theories. Рart 1 Book in PDF, ePub and Kindle
The book is the first part of the monograph “Classification of countable models of complete theories” consisting of two parts. In the monograph, a classification of countable models of complete theories with respect to two basic characteristics (Rudin–Keisler preorders and distribution functions for numbers of limit models) is presented and applied to the most important classes of countable theories such as the class of Ehrenfeucht theories (i. e., complete first-order theories with finitely many but more than one pairwise non-isomorphic countable models), the class of small theories (i. e., complete first-order theories with countably many types), and the class of countable first-order theories with continuum many types. For realizations of basic characteristics of countable complete theories, syntactic generic constructions, generalizing the Jonsson–Fraïssé construction and the Hrushovski construction, are presented. Using these constructions a solution of the Goncharov–Millar problem (on the existence of Ehrenfeucht theories with countable models which are not almost homogeneous) is described. Modifying the Hrushovski–Herwig generic construction, a solution of the Lachlan problem on the existence of stable Ehrenfeucht theories is shown. In the first part, a characterization of Ehrenfeuchtness, properties of Ehrenfeucht theories, generic constructions, and algebras for distributions of binary semi-isolating formulas of a complete theory are considered.The book is intended for specialists interested in Mathematical Logic.
| Author | : Sergey Sudoplatov |
| Publisher | : Litres |
| Total Pages | : 394 |
| Release | : 2022-01-29 |
| Genre | : Mathematics |
| ISBN | : 5041454795 |
Download Classification of countable models of complete theories. Рart 2 Book in PDF, ePub and Kindle
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. |
| Total Pages | : 132 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821897454 |
Download Uncountably Categorical Theories Book in PDF, ePub and Kindle
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 | : Wilfrid Hodges |
| Publisher | : Cambridge University Press |
| Total Pages | : 322 |
| Release | : 1997-04-10 |
| Genre | : Mathematics |
| ISBN | : 9780521587136 |
Download A Shorter Model Theory Book in PDF, ePub and Kindle
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 |
| Total Pages | : 402 |
| Release | : 1988-02-25 |
| Genre | : Mathematics |
| ISBN | : 0521348331 |
Download Model Theory and Modules Book in PDF, ePub and Kindle
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 | : Viggo Stoltenberg-Hansen |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2017-03-30 |
| Genre | : Mathematics |
| ISBN | : 1108587143 |
Download Logic Colloquium '03 Book in PDF, ePub and Kindle
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fourth publication in the Lecture Notes in Logic series, contains the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Helsinki, Finland, in August 2003. These articles include an extended tutorial on generalizing finite model theory, as well as seventeen original research articles spanning all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy.
| Author | : John T. Baldwin |
| Publisher | : Springer |
| Total Pages | : 512 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540480498 |
Download Classification Theory Book in PDF, ePub and Kindle
| Author | : Ali Enayat |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 184 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821835351 |
Download Nonstandard Models of Arithmetic and Set Theory Book in PDF, ePub and Kindle
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. |
| Total Pages | : 92 |
| Release | : 2014-06-05 |
| Genre | : Mathematics |
| ISBN | : 0821894757 |
Download Generalized Descriptive Set Theory and Classification Theory Book in PDF, ePub and Kindle
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.
| Author | : O.V. Belegradek |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780821896037 |
Download Model Theory and Applications Book in PDF, ePub and Kindle
This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.
