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Author : Thomas J. Jech
Publisher : Unknown
Page : 137 pages
File Size : 53,7 Mb
Release : 1971
Category : Set theory
ISBN : OCLC:969994548
Author : Thomas J. Jech
Publisher : Springer
Page : 142 pages
File Size : 55,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540368823
Author : Andrej Ščedrov
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 49,6 Mb
Release : 1984
Category : Categories
ISBN : 9780821822944
We give a general method of forcing over categories as a category-theoretic universal construction which subsumes, on one hand, all known instances of forcing in set theory, Boolean and Heyting valued models and sheaf interpretations for both classical and intuitionistic formal systems; and, on the other hand, constructions of classifying topoi in topos theory.
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512336
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Author : Y.N. Moschovakis
Publisher : Elsevier
Page : 636 pages
File Size : 51,6 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 9780080963198
Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.
Author : A.A. Fraenkel,Y. Bar-Hillel,A. Levy
Publisher : Elsevier
Page : 415 pages
File Size : 51,6 Mb
Release : 1973-12-01
Category : Computers
ISBN : 9780080887050
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.
Author : Thomas Jech
Publisher : Springer Science & Business Media
Page : 772 pages
File Size : 50,5 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 9783540447610
This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory....The present ‘Third Millennium’ edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS
Author : Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 45,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475743852
1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.
Author : M. Hazewinkel
Publisher : Springer
Page : 927 pages
File Size : 50,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489937971
Author : Nikolai Konstantinovich Vereshchagin,Alexander Shen
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 46,5 Mb
Release : 2002
Category : Set theory
ISBN : 9780821827314
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Author : D.L. Colton,R.P. Gilbert
Publisher : Springer
Page : 488 pages
File Size : 45,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540373025
Author : R. Bott,S. Gitler
Publisher : Springer
Page : 183 pages
File Size : 54,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540376163
Author : Valeriy K. Zakharov,Timofey V. Rodionov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 446 pages
File Size : 52,5 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110550214
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
Author : A.G. Kusraev,Semën Samsonovich Kutateladze
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401144438
Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
Author : P. Erdös,A. Máté,A. Hajnal,P. Rado
Publisher : Elsevier
Page : 349 pages
File Size : 53,6 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 9780444537454
This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.
