Beginning Model Theory PDF Download
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Author: Jane Bridge
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 162
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Book Description
Author: Jane Bridge
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 162
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Book Description
Author: David Marker
Publisher: Springer Science & Business Media
ISBN: 0387227342
Category : Mathematics
Languages : en
Pages : 342
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Book Description
Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
Author: Bruno Poizat
Publisher: Springer Science & Business Media
ISBN: 1441986227
Category : Mathematics
Languages : en
Pages : 472
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Book Description
Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.
Author: Jonathan Kirby
Publisher: Cambridge University Press
ISBN: 1316732398
Category : Mathematics
Languages : en
Pages : 197
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Book Description
Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
Author: Roman Kossak
Publisher:
ISBN: 9781848903616
Category :
Languages : en
Pages : 152
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Book Description
This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.
Author: Tim Button
Publisher: Oxford University Press
ISBN: 0198790392
Category : Mathematics
Languages : en
Pages : 534
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Book Description
Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.
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: Thomas Metzinger
Publisher: MIT Press
ISBN: 0262263807
Category : Medical
Languages : en
Pages : 903
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Book Description
According to Thomas Metzinger, no such things as selves exist in the world: nobody ever had or was a self. All that exists are phenomenal selves, as they appear in conscious experience. The phenomenal self, however, is not a thing but an ongoing process; it is the content of a "transparent self-model." In Being No One, Metzinger, a German philosopher, draws strongly on neuroscientific research to present a representationalist and functional analysis of what a consciously experienced first-person perspective actually is. Building a bridge between the humanities and the empirical sciences of the mind, he develops new conceptual toolkits and metaphors; uses case studies of unusual states of mind such as agnosia, neglect, blindsight, and hallucinations; and offers new sets of multilevel constraints for the concept of consciousness. Metzinger's central question is: How exactly does strong, consciously experienced subjectivity emerge out of objective events in the natural world? His epistemic goal is to determine whether conscious experience, in particular the experience of being someone that results from the emergence of a phenomenal self, can be analyzed on subpersonal levels of description. He also asks if and how our Cartesian intuitions that subjective experiences as such can never be reductively explained are themselves ultimately rooted in the deeper representational structure of our conscious minds.
Author: Jerome Malitz
Publisher: Springer Science & Business Media
ISBN: 1461394414
Category : Mathematics
Languages : en
Pages : 209
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Book Description
This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.
Author: Martin J. Osborne
Publisher: Open Book Publishers
ISBN: 180511123X
Category : Business & Economics
Languages : en
Pages : 382
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Book Description
Models in Microeconomic Theory covers basic models in current microeconomic theory. Part I (Chapters 1-7) presents models of an economic agent, discussing abstract models of preferences, choice, and decision making under uncertainty, before turning to models of the consumer, the producer, and monopoly. Part II (Chapters 8-14) introduces the concept of equilibrium, beginning, unconventionally, with the models of the jungle and an economy with indivisible goods, and continuing with models of an exchange economy, equilibrium with rational expectations, and an economy with asymmetric information. Part III (Chapters 15-16) provides an introduction to game theory, covering strategic and extensive games and the concepts of Nash equilibrium and subgame perfect equilibrium. Part IV (Chapters 17-20) gives a taste of the topics of mechanism design, matching, the axiomatic analysis of economic systems, and social choice. The book focuses on the concepts of model and equilibrium. It states models and results precisely, and provides proofs for all results. It uses only elementary mathematics (with almost no calculus), although many of the proofs involve sustained logical arguments. It includes about 150 exercises. With its formal but accessible style, this textbook is designed for undergraduate students of microeconomics at intermediate and advanced levels.
