A Shorter Model Theory

A Shorter Model Theory
Author: Wilfrid Hodges
Publisher: Cambridge University Press
Total Pages: 322
Release: 1997-04-10
Genre: Mathematics
ISBN: 9780521587136

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.

Model Theory

Model Theory
Author: Wilfrid Hodges
Publisher: Cambridge University Press
Total Pages: 810
Release: 1993-03-11
Genre: Mathematics
ISBN: 9780521304429

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.

An Invitation to Model Theory

An Invitation to Model Theory
Author: Jonathan Kirby
Publisher: Cambridge University Press
Total Pages: 197
Release: 2019-04-18
Genre: Mathematics
ISBN: 1316732398

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.

A Course in Model Theory

A Course in Model Theory
Author: Katrin Tent
Publisher: Cambridge University Press
Total Pages: 259
Release: 2012-03-08
Genre: Mathematics
ISBN: 052176324X

Concise introduction to current topics in model theory, including simple and stable theories.

Being No One

Being No One
Author: Thomas Metzinger
Publisher: MIT Press
Total Pages: 896
Release: 2004-08-20
Genre: Medical
ISBN: 0262263807

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.

Model Theory : An Introduction

Model Theory : An Introduction
Author: David Marker
Publisher: Springer Science & Business Media
Total Pages: 342
Release: 2006-04-06
Genre: Mathematics
ISBN: 0387227342

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

Classification Theory

Classification Theory
Author: S. Shelah
Publisher: Elsevier
Total Pages: 741
Release: 1990-12-06
Genre: Computers
ISBN: 008088024X

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

Linear Model Theory

Linear Model Theory
Author: Dale L. Zimmerman
Publisher: Springer Nature
Total Pages: 504
Release: 2020-11-02
Genre: Mathematics
ISBN: 3030520633

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.

Theory of Continuous Groups

Theory of Continuous Groups
Author: Charles Loewner
Publisher: Courier Corporation
Total Pages: 128
Release: 2008-01-01
Genre: Mathematics
ISBN: 0486462927

Based on lectures by a renowned educator, this book focuses on continuous groups, particularly in terms of applications in geometry and analysis. The author's unique perspectives are illustrated by numerous inventive geometric examples, many of which were inspired by footnotes among the work of Sophus Lie. 1971 edition.