CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS EDITORIAL BOARD B. BOLLOBAS , W. FULTON , A. KATOK , F. KIRWAN , P. SARNAK Lectures in Logic and Set Theory Volume 2 This two - volume work bridges the gap between introductory expositions of ...
Author: George Tourlakis
Publisher: Cambridge University Press
ISBN: 113943943X
Category: Mathematics
Page: 596
View: 152
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 EDITORIAL BOARD B. BOLLOBAS, W. FULTON, A. KATOK, F. KIRWAN, P. SARNAK Lectures in Logic and Set Theory Volume 1 This two-volume work bridges the gap between introductory expositions of logic or ...
Author: George Tourlakis
Publisher: Cambridge University Press
ISBN: 9781139439428
Category: Mathematics
Page: 328
View: 361
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.
Papers from the AMS - ASL Joint Special Session “ Interactions between Logic , Group Theory and Computer Science ” held in ... ( Editors ) 2005b : 20003 20-06 ( 20E05 , 68 -06 ) - * Nonstandard models of arithmetic and set theory .
Monadic operators defined by means of propositional quantification in intuitionistic logic. ... Set Theory with an Introduction to Descriptive Set Theory, volume 86 of Studies in Logic and the Foundations of Mathematics.
Author: Morten Heine Sørensen
Publisher: Elsevier
ISBN: 0080478921
Category: Mathematics
Page: 456
View: 234
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning
G. Tourlakis : Lectures in Logic and Set Theory . Volume 2 : Set Theory . ( Cambridge studies in advanced mathematics 83 ) . Cambridge University Press , 2003 , XV + 575 S. ISBN 0-521-75374-0 H / b £ 65 , - . Band 2 kann unabhängig von ...
Author:
Publisher:
ISBN: CORNELL:31924099691044
Category: Mathematics
Page:
View: 469
Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.
Cambridge Studies in Advanced Mathematics 59, Cambridge University Press, 1999. hibault, 19821 M.-F. Thibault. Prerecursive categories. J. Pure Appl. Algebra, 24, 7993, 1982. ierney, 19721 M. Tierney. Sheaf theory and the continuum ...
Author: D.M. Gabbay
Publisher: Springer Science & Business Media
ISBN: 9781402030925
Category: Philosophy
Page: 372
View: 699
The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications
15. D. J. Struik, “Lectures on Classical Differential Geometry,” Addison-Wesley Publishing Company, Inc., Cambridge, Mass, 1950. Algebra 16. A. A. Albert (ed.), “Studies in Modern Algebra,” vol. 2 in Math. Assoc. of America, “Studies in ...
Author: R. Creighton Buck
Publisher: Waveland Press
ISBN: 9781478608202
Category: Mathematics
Page: 622
View: 913
Demonstrating analytical and numerical techniques for attacking problems in the application of mathematics, this well-organized, clearly written text presents the logical relationship and fundamental notations of analysis. Buck discusses analysis not solely as a tool, but as a subject in its own right. This skill-building volume familiarizes students with the language, concepts, and standard theorems of analysis, preparing them to read the mathematical literature on their own. The text revisits certain portions of elementary calculus and gives a systematic, modern approach to the differential and integral calculus of functions and transformations in several variables, including an introduction to the theory of differential forms. The material is structured to benefit those students whose interests lean toward either research in mathematics or its applications.
Then , after recovering from an incapacitating bout of depression , he turned to set theory . ... From Frege to Gödel : A Source Book in Mathematical Logic , 1879-1931 , Cambridge , MA : Harvard University Press , 1967 , 582-91 .
Author: Routledge (Firm)
Publisher: Taylor & Francis
ISBN: 0415073103
Category: Reference
Page: 896
View: 511
Contains a full index of all the topics covered in the first nine volumes of the set.
Release on 1977 | by Environmental Science Information Center. Library and Information Services Division
1. Spline theory Addresses , essays , lectures . 2 . Approximation theory – Addresses , essays , lectures . I. Greville , Thomas Nall Eden , 1910- ed . ( S : United States . Army . Mathematics Research Center , Madison , Wis .
Author: Environmental Science Information Center. Library and Information Services Division
7 ALGEBRAIC LOGIC AND MATHEMATICAL LOGIC Quite obviously, algebraic logic is mathematical logic in one sense of that ... For example, Peirce's set theory, though not Cantorean, was mathematically sophisticated and was developed with ...
Author: Ivor Grattan-Guiness
Publisher: Routledge
ISBN: 9781134887552
Category: History
Page: 571
View: 540
First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
Release on 1977 | by Environmental Science Information Center. Library and Information Services Division
1. Spline theory Addresses , essays , lectures . 2 . Approximation theory - Addresses , essays , lectures . I. Greville , Thomas Nall Eden , 1910- ed . ( S : United States . Army . Mathematics Research Center , Madison , Wis .
Author: Environmental Science Information Center. Library and Information Services Division
J. Math. 19 (1944), 57-71. T. Jech, Set Theory”, Academic Press, 1978. xi+621 p. G. Jenča, A Cantor-Bernstein type theorem ... Vol. II: Advanced Theory”. Grad. Studies in Math. 16, Amer. Math. Soc., Providence, 1977. xxii-Hpp. 399–1074.
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 9780821837160
Category: Mathematics
Page: 117
View: 347
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory.
Author: Joachim Lambek
Publisher:
ISBN: 0521246652
Category: Mathematics
Page: 293
View: 555
In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic type theories) is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines.
Cited in BCL3 and Sheehy . Formerly Books in series in the United States . The editor's solicitude expressed in the preface Bowker...has consistently recognized those areas in which we can assist to make the work of librarians...easier. It is because of this concern that we decided to publish the 1
This book offers a new algebraic approach to set theory.
Author: Andri Joyal
Publisher: Cambridge University Press
ISBN: 0521558301
Category: Mathematics
Page: 136
View: 872
This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
Lectures in Logic and Set Theory Volume 2 : Set Theory GEORGE TOURLARIS G. Tourlakis Lectures in Logic and Set Theory Volume 1 : Mathematical Logic , Volume 2 : Set Theory Cambridge Studies in Advanced Mathematics , Nos 82 ...
Fuzzy sets . 2. Fuzzy logic . 3. Fuzzy mathematics . 4 . Data mining . 5. Soft computing . I. Title . II . ... Point set theory . 2. ... ( Cambridge studies in advanced mathematics ; 105 ) Includes bibliographical references ( p .