Lectures in Logic and Set Theory: Volume 2, Set Theory

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Author: George Tourlakis

Publisher: Cambridge University Press

ISBN: 9781139439435

Category: Mathematics

Page: N.A

View: 8860

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

Fundamentals of Set and Number Theory

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Author: Valeriy K. Zakharov,Timofey V. Rodionov

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110550946

Category: Mathematics

Page: 446

View: 2167

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

Fundamentals of Functions and Measure Theory

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Author: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110550962

Category: Mathematics

Page: 478

View: 2105

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals

Lectures in Logic and Set Theory: Volume 1, Mathematical Logic

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Author: George Tourlakis

Publisher: Cambridge University Press

ISBN: 9781139439428

Category: Mathematics

Page: N.A

View: 2506

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.

Introduction to Foliations and Lie Groupoids

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Author: I. Moerdijk,J. Mrcun

Publisher: Cambridge University Press

ISBN: 9781139438988

Category: Mathematics

Page: N.A

View: 3217

This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture

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Author: Joel Friedman

Publisher: American Mathematical Soc.

ISBN: 1470409887

Category: Mathematics

Page: 106

View: 3651

In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.

Games, Scales and Suslin Cardinals: The Cabal Seminar

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Author: A. S. Kechris,Benedikt Lwe,John R. Steel

Publisher: Cambridge University Press

ISBN: 0521899516

Category: Mathematics

Page: 445

View: 5142

Presents seminal papers from the Caltech-UCLA 'Cabal Seminar', unpublished material, and related new papers.

Principia Mathematica.

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Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 1465

Books in Series

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Author: N.A

Publisher: N.A

ISBN: 9780835221092

Category: Monographic series

Page: 1756

View: 1837

The Core Model Iterability Problem

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Author: John R. Steel

Publisher: Cambridge University Press

ISBN: 1107167965

Category: Mathematics

Page: 118

View: 2255

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. Large cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or 'core models', satisfying them. Since Gödel's pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. In this volume, the eighth publication in the Lecture Notes in Logic series, Steel extends this theory so that it can produce core models having Woodin cardinals, a large cardinal hypothesis that is the focus of much current research. The book is intended for advanced graduate students and researchers in set theory.

Metamathematics of First-Order Arithmetic

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Author: Petr Hájek,Pavel Pudlák

Publisher: Cambridge University Press

ISBN: 1107168414

Category: Mathematics

Page: 474

View: 9615

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 third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

The Cambridge Companion to Greek and Roman Theatre

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Author: Marianne McDonald,Michael Walton

Publisher: Cambridge University Press

ISBN: 1139827251

Category: Drama

Page: N.A

View: 953

This series of essays by prominent academics and practitioners investigates in detail the history of performance in the classical Greek and Roman world. Beginning with the earliest examples of 'dramatic' presentation in the epic cycles and reaching through to the latter days of the Roman Empire and beyond, this 2007 Companion covers many aspects of these broad presentational societies. Dramatic performances that are text-based form only one part of cultures where presentation is a major element of all social and political life. Individual chapters range across a two thousand year timescale, and include specific chapters on acting traditions, masks, properties, playing places, festivals, religion and drama, comedy and society, and commodity, concluding with the dramatic legacy of myth and the modern media. The book addresses the needs of students of drama and classics, as well as anyone with an interest in the theatre's history and practice.

Books in Print

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Author: R.R. Bowker Company

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 3851

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

The Evolution of Logic

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Author: W. D. Hart

Publisher: Cambridge University Press

ISBN: 1139491202

Category: Philosophy

Page: N.A

View: 5133

Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.