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


Author: George Tourlakis
Publisher: Cambridge University Press
ISBN: 9781139439435
Category: Mathematics
Page: N.A
View: 350
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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


Author: Valeriy K. Zakharov,Timofey V. Rodionov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110550946
Category: Mathematics
Page: 446
View: 6302
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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

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


Author: George Tourlakis
Publisher: Cambridge University Press
ISBN: 9781139439428
Category: Mathematics
Page: N.A
View: 5297
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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.

Einführung in die Kategorientheorie

Mit ausführlichen Erklärungen und zahlreichen Beispielen
Author: Martin Brandenburg
Publisher: Springer-Verlag
ISBN: 3662535211
Category: Mathematics
Page: 343
View: 1013
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Die Kategorientheorie deckt die innere Architektur der Mathematik auf. Dabei werden die strukturellen Gemeinsamkeiten zwischen mathematischen Disziplinen und ihren spezifischen Konstruktionen herausgearbeitet. Dieses Buch gibt eine systematische Einführung in die Grundbegriffe der Kategorientheorie. Zahlreiche ausführliche Erklärungstexte sowie die große Menge an Beispielen helfen beim Einstieg in diese verhältnismäßig abstrakte Theorie. Es werden viele konkrete Anwendungen besprochen, welche die Nützlichkeit der Kategorientheorie im mathematischen Alltag belegen. Jedes Kapitel wird mit einem motivierenden Text eingeleitet und mit einer großen Aufgabensammlung abgeschlossen. An Vorwissen muss der Leser lediglich ein paar Grundbegriffe des Mathematik-Studiums mitbringen. Die vorliegende zweite vollständig durchgesehene Auflage ist um ausführliche Lösungen zu ausgewählten Aufgaben ergänzt.

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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Sets and Extensions in the Twentieth Century


Author: N.A
Publisher: Elsevier
ISBN: 0080930662
Category: Mathematics
Page: 880
View: 9257
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Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights

Introduction to Foliations and Lie Groupoids


Author: I. Moerdijk,J. Mrcun
Publisher: Cambridge University Press
ISBN: 9781139438988
Category: Mathematics
Page: N.A
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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


Author: Joel Friedman
Publisher: American Mathematical Soc.
ISBN: 1470409887
Category: Mathematics
Page: 106
View: 9876
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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


Author: A. S. Kechris,Benedikt Lwe,John R. Steel
Publisher: Cambridge University Press
ISBN: 0521899516
Category: Mathematics
Page: 445
View: 6780
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Presents seminal papers from the Caltech-UCLA 'Cabal Seminar', unpublished material, and related new papers.

Principia Mathematica.


Author: Alfred North Whitehead,Bertrand Russell
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: 167
View: 1370
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Books in Series


Author: N.A
Publisher: N.A
ISBN: 9780835221092
Category: Monographic series
Page: 1756
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American Book Publishing Record


Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 3412
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The Core Model Iterability Problem


Author: John R. Steel
Publisher: Cambridge University Press
ISBN: 1107167965
Category: Mathematics
Page: 118
View: 5417
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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.

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual
Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
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American Book Publishing Record

BPR annual cumulative
Author: Bowker Staff
Publisher: R. R. Bowker
ISBN: N.A
Category: United States
Page: N.A
View: 5718
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The British National Bibliography


Author: Arthur James Wells
Publisher: N.A
ISBN: N.A
Category: English literature
Page: N.A
View: 2988
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Neue Topologische Methoden in der Algebraischen Geometrie


Author: Friedrich Hirzebruch
Publisher: Springer-Verlag
ISBN: 3662410834
Category: Mathematics
Page: 165
View: 1033
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The Descriptive Set Theory of Polish Group Actions


Author: Howard Becker,A. S. Kechris
Publisher: Cambridge University Press
ISBN: 9780521576055
Category: Mathematics
Page: 136
View: 7251
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Research monograph on set theory by two of the world's leading researchers.

Metamathematics of First-Order Arithmetic


Author: Petr Hájek,Pavel Pudlák
Publisher: Cambridge University Press
ISBN: 1107168414
Category: Mathematics
Page: 474
View: 1418
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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


Author: Marianne McDonald,Michael Walton
Publisher: Cambridge University Press
ISBN: 1139827251
Category: Drama
Page: N.A
View: 7467
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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.