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Author : Jane Bridge
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.3/5 (91 download)
Download or read book Beginning Model Theory written by Jane Bridge and published by Oxford University Press, USA. This book was released on 1977 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Marker
Publisher : Springer Science & Business Media
ISBN 13 : 0387227342
Total Pages : 342 pages
Book Rating : 4.3/5 (872 download)
Download or read book Model Theory : An Introduction written by David Marker and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Roman Kossak
Publisher :
ISBN 13 : 9781848903616
Total Pages : 152 pages
Book Rating : 4.9/5 (36 download)
Download or read book Model Theory for Beginners. 15 Lectures written by Roman Kossak and published by . This book was released on 2021-02-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jonathan Kirby
Publisher : Cambridge University Press
ISBN 13 : 1316732398
Total Pages : 197 pages
Book Rating : 4.3/5 (167 download)
Download or read book An Invitation to Model Theory written by Jonathan Kirby and published by Cambridge University Press. This book was released on 2019-04-18 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bruno Poizat
Publisher : Springer Science & Business Media
ISBN 13 : 1441986227
Total Pages : 472 pages
Book Rating : 4.4/5 (419 download)
Download or read book A Course in Model Theory written by Bruno Poizat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Tim Button
Publisher : Oxford University Press
ISBN 13 : 0198790392
Total Pages : 534 pages
Book Rating : 4.1/5 (987 download)
Download or read book Philosophy and Model Theory written by Tim Button and published by Oxford University Press. This book was released on 2018 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Thomas Metzinger
Publisher : MIT Press
ISBN 13 : 0262263807
Total Pages : 903 pages
Book Rating : 4.2/5 (622 download)
Download or read book Being No One written by Thomas Metzinger and published by MIT Press. This book was released on 2004-08-20 with total page 903 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Wilfrid Hodges
Publisher : Cambridge University Press
ISBN 13 : 9780521587136
Total Pages : 322 pages
Book Rating : 4.5/5 (871 download)
Download or read book A Shorter Model Theory written by Wilfrid Hodges and published by Cambridge University Press. This book was released on 1997-04-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jerome Malitz
Publisher : Springer Science & Business Media
ISBN 13 : 1461394414
Total Pages : 209 pages
Book Rating : 4.4/5 (613 download)
Download or read book Introduction to Mathematical Logic written by Jerome Malitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 180511123X
Total Pages : 382 pages
Book Rating : 4.8/5 (51 download)
Download or read book Models in Microeconomic Theory written by Martin J. Osborne and published by Open Book Publishers. This book was released on 2023-06-26 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Dale L. Zimmerman
Publisher : Springer Nature
ISBN 13 : 3030520633
Total Pages : 504 pages
Book Rating : 4.0/5 (35 download)
Download or read book Linear Model Theory written by Dale L. Zimmerman and published by Springer Nature. This book was released on 2020-11-02 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.
Author : Matthias Aschenbrenner
Publisher : Princeton University Press
ISBN 13 : 0691175438
Total Pages : 873 pages
Book Rating : 4.6/5 (911 download)
Download or read book Asymptotic Differential Algebra and Model Theory of Transseries written by Matthias Aschenbrenner and published by Princeton University Press. This book was released on 2017-06-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Author : Philipp Rothmaler
Publisher : CRC Press
ISBN 13 : 9789056992873
Total Pages : 334 pages
Book Rating : 4.9/5 (928 download)
Download or read book Introduction to Model Theory written by Philipp Rothmaler and published by CRC Press. This book was released on 2000-10-31 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gerald E. Sacks
Publisher : Addison Wesley Longman
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.3/5 (91 download)
Download or read book Saturated Model Theory written by Gerald E. Sacks and published by Addison Wesley Longman. This book was released on 1972 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John T. Baldwin
Publisher : Cambridge University Press
ISBN 13 : 1107189217
Total Pages : 365 pages
Book Rating : 4.1/5 (71 download)
Download or read book Model Theory and the Philosophy of Mathematical Practice written by John T. Baldwin and published by Cambridge University Press. This book was released on 2018-01-25 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
Author : George J Mailath
Publisher : World Scientific
ISBN 13 : 9813239956
Total Pages : 364 pages
Book Rating : 4.8/5 (132 download)
Download or read book Modeling Strategic Behavior: A Graduate Introduction To Game Theory And Mechanism Design written by George J Mailath and published by World Scientific. This book was released on 2018-12-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is impossible to understand modern economics without knowledge of the basic tools of gametheory and mechanism design. This book provides a graduate-level introduction to the economic modeling of strategic behavior. The goal is to teach Economics doctoral students the tools of game theory and mechanism design that all economists should know.
Author : Matthew Foreman
Publisher : Springer Science & Business Media
ISBN 13 : 1402057644
Total Pages : 2200 pages
Book Rating : 4.4/5 (2 download)
Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
