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Author: Michael Chris Laskowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 156
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Book Description
Author: Michael Chris Laskowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 156
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Book Description
Author: Philipp Rothmaler
Publisher: CRC Press
ISBN: 0429668503
Category : Mathematics
Languages : en
Pages : 324
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Book Description
Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
Author: Steven Buechler
Publisher: Cambridge University Press
ISBN: 1107168392
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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. Stability theory was introduced and matured in the 1960s and 1970s. Today stability theory influences and is influenced by number theory, algebraic group theory, Riemann surfaces, and representation theory of modules. There is little model theory today that does not involve the methods of stability theory. In this volume, the fourth publication in the Perspectives in Logic series, Steven Buechler bridges the gap between a first-year graduate logic course and research papers in stability theory. The book prepares the student for research in any of today's branches of stability theory, and gives an introduction to classification theory with an exposition of Morley's Categoricity Theorem.
Author: John T. Baldwin
Publisher: Cambridge University Press
ISBN: 1107168090
Category : Mathematics
Languages : en
Pages : 462
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Book Description
This book introduces first order stability theory, organized around the spectrum problem, with complete proofs of the Vaught conjecture for ω-stable theories.
Author: John T. Baldwin
Publisher: Springer
ISBN: 3540480498
Category : Mathematics
Languages : en
Pages : 512
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Book Description
Author: Gerald E. Sacks
Publisher: World Scientific
ISBN: 9789812564894
Category : Mathematics
Languages : en
Pages : 712
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Book Description
This invaluable book is a collection of 31 important both inideas and results papers published by mathematical logicians inthe 20th Century. The papers have been selected by Professor Gerald ESacks. Some of the authors are Gdel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin.
Author: Wilfrid Hodges
Publisher: Cambridge University Press
ISBN: 9780521304429
Category : Mathematics
Languages : en
Pages : 810
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Book Description
Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
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: Cambridge University Press
ISBN: 1107189217
Category : Mathematics
Languages : en
Pages : 365
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Book Description
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
Author: C.C. Chang
Publisher: Courier Corporation
ISBN: 0486310957
Category : Mathematics
Languages : en
Pages : 674
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Book Description
This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.
