The Consistency Of The Axiom Of Choice And Of The Generalized Continuum Hypothesis With The Axioms Of Set Theory

Author : Kurt Gödel
Publisher : Princeton University Press
ISBN 13 : 0691079277
Total Pages : 80 pages
Book Rating : 4.71/5 ( download)

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Download or read book The Consistency of the Axiom of Choice and of the Generalized Continuum-hypothesis with the Axioms of Set Theory written by Kurt Gödel and published by Princeton University Press. This book was released on 1940 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Kurt Gödel
Publisher :
ISBN 13 :
Total Pages : 69 pages
Book Rating : 4.17/5 ( download)

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Download or read book The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory written by Kurt Gödel and published by . This book was released on 1953 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher :
ISBN 13 :
Total Pages : 69 pages
Book Rating : 4.31/5 ( download)

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Download or read book The Consistency of the Axiom of Choice and of the Generalized Continuum-hypothesis with the Axioms of Set Theory written by and published by . This book was released on 1940 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Kurt Gödel
Publisher :
ISBN 13 :
Total Pages : 69 pages
Book Rating : 4.53/5 ( download)

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Download or read book The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory. (Second Printing.). written by Kurt Gödel and published by . This book was released on 1940 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : A.A. Fraenkel
Publisher : Elsevier
ISBN 13 : 0080887058
Total Pages : 415 pages
Book Rating : 4.50/5 ( download)

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Download or read book Foundations of Set Theory written by A.A. Fraenkel and published by Elsevier. This book was released on 1973-12-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Barnaby Sheppard
Publisher : Cambridge University Press
ISBN 13 : 1139952773
Total Pages : 498 pages
Book Rating : 4.74/5 ( download)

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Download or read book The Logic of Infinity written by Barnaby Sheppard and published by Cambridge University Press. This book was released on 2014-07-24 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

Author : Yiannis N. Moschovakis
Publisher : American Mathematical Soc.
ISBN 13 : 0821848135
Total Pages : 521 pages
Book Rating : 4.35/5 ( download)

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Download or read book Descriptive Set Theory written by Yiannis N. Moschovakis and published by American Mathematical Soc.. This book was released on 2009-06-30 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.

Author : Lorenz J. Halbeisen
Publisher : Springer Science & Business Media
ISBN 13 : 9781447121732
Total Pages : 456 pages
Book Rating : 4.32/5 ( download)

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Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Author : Kurt Gödel
Publisher :
ISBN 13 : 0195039726
Total Pages : 426 pages
Book Rating : 4.26/5 ( download)

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Download or read book Publications 1929-1936 written by Kurt Gödel and published by . This book was released on 1986 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 9780080954943
Total Pages : 357 pages
Book Rating : 4.44/5 ( download)

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Download or read book Provability, Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection