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: 7810
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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.

Cambridge Studies in Advanced Mathematics


Author: George J. Tourlakis
Publisher: N.A
ISBN: 9780521753746
Category: Logic, Symbolic and mathematical
Page: N.A
View: 4200
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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: 2522
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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.

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: 1762
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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

Fundamentals of Functions and Measure Theory


Author: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110550962
Category: Mathematics
Page: 478
View: 6747
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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 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

Einführung in die Kategorientheorie

Mit ausführlichen Erklärungen und zahlreichen Beispielen
Author: Martin Brandenburg
Publisher: Springer-Verlag
ISBN: 3662535211
Category: Mathematics
Page: 343
View: 9435
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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
View: 9008
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Introduction to Foliations and Lie Groupoids


Author: I. Moerdijk,J. Mrcun
Publisher: Cambridge University Press
ISBN: 9781139438988
Category: Mathematics
Page: N.A
View: 9511
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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.

Principia Mathematica.


Author: Alfred North Whitehead,Bertrand Russell
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: 167
View: 6586
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Lecture notes in pure and applied mathematics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 5878
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Topics in Algebraic Graph Theory


Author: Lowell W. Beineke,Robin J. Wilson
Publisher: Cambridge University Press
ISBN: 9780521801973
Category: Mathematics
Page: 276
View: 6763
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There is no other book with such a wide scope of both areas of algebraic graph theory.

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: 2256
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Presents seminal papers from the Caltech-UCLA 'Cabal Seminar', unpublished material, and related new papers.

The Core Model Iterability Problem


Author: John R. Steel
Publisher: Cambridge University Press
ISBN: 1107167965
Category: Mathematics
Page: 118
View: 3470
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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.

Landmark Writings in Western Mathematics 1640-1940


Author: Ivor Grattan-Guinness
Publisher: Elsevier
ISBN: 9780080457444
Category: Mathematics
Page: 1040
View: 7468
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This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. First book of its kind Covers the period 1640-1940 of massive development in mathematics Describes many of the main writings of mathematics Articles written by specialists in their field

Essential Stability Theory


Author: Steven Buechler
Publisher: Cambridge University Press
ISBN: 1107168392
Category: Mathematics
Page: 367
View: 6834
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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. Stability theory was introduced and matured in the 1960s and 1970s. Today stability theory influences and is influenced by number theory, algebraic group theory, Riemann surfaces, and representation theory of modules. There is little model theory today that does not involve the methods of stability theory. In this volume, the fourth publication in the Perspectives in Logic series, Steven Buechler bridges the gap between a first-year graduate logic course and research papers in stability theory. The book prepares the student for research in any of today's branches of stability theory, and gives an introduction to classification theory with an exposition of Morley's Categoricity Theorem.

Books in Series


Author: N.A
Publisher: N.A
ISBN: 9780835221092
Category: Monographic series
Page: 1756
View: 5355
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Metamathematics of First-Order Arithmetic


Author: Petr Hájek,Pavel Pudlák
Publisher: Cambridge University Press
ISBN: 1107168414
Category: Mathematics
Page: 474
View: 1745
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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).

A Course in Modern Mathematical Physics

Groups, Hilbert Space and Differential Geometry
Author: Peter Szekeres
Publisher: Cambridge University Press
ISBN: 9780521829601
Category: Mathematics
Page: 600
View: 6516
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This book provides an introduction to the mathematics of modern physics, presenting concepts and techniques in mathematical physics at a level suitable for advanced undergraduates and beginning graduate students. It aims to introduce the reader to modern mathematical thinking within a physics setting. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book includes exercises and worked examples, to test the students' understanding of the various concepts, as well as extending the themes covered in the main text.

American Book Publishing Record


Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 9123
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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: 850
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Research monograph on set theory by two of the world's leading researchers.