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Introduction to Axiomatic Set Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 681/5 ( reviews)

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Book Synopsis Introduction to Axiomatic Set Theory by : G. Takeuti

Download or read book Introduction to Axiomatic Set Theory written by G. Takeuti. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are high lighted, and second, the student who wishes to master the subject is com pelled to develop the detail on his own. However, an instructor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text.

Axiomatic Set Theory

2012-05-04 Mathematics
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Release : 2012-05-04
Genre : Mathematics
Kind : eBook
Book Rating : 876/5 ( reviews)

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Book Synopsis Axiomatic Set Theory by : Patrick Suppes

Download or read book Axiomatic Set Theory written by Patrick Suppes. This book was released on 2012-05-04. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

Introduction to Axiomatic Set Theory

1969 Axiomatic set theory
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Release : 1969
Genre : Axiomatic set theory
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Introduction to Axiomatic Set Theory by : Edward John Lemmon

Download or read book Introduction to Axiomatic Set Theory written by Edward John Lemmon. This book was released on 1969. Available in PDF, EPUB and Kindle. Book excerpt:

Set Theory and its Philosophy

2004-01-15 Philosophy
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Release : 2004-01-15
Genre : Philosophy
Kind : eBook
Book Rating : 432/5 ( reviews)

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Book Synopsis Set Theory and its Philosophy by : Michael Potter

Download or read book Set Theory and its Philosophy written by Michael Potter. This book was released on 2004-01-15. Available in PDF, EPUB and Kindle. Book excerpt: Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Introduction to Axiomatic Set Theory

2012-12-06 Philosophy
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Release : 2012-12-06
Genre : Philosophy
Kind : eBook
Book Rating : 444/5 ( reviews)

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Book Synopsis Introduction to Axiomatic Set Theory by : J.L. Krivine

Download or read book Introduction to Axiomatic Set Theory written by J.L. Krivine. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the classic relative consistency proofs in set theory that are obtained by the device of 'inner models'. Three examples of such models are investigated in Chapters VI, VII, and VIII; the most important of these, the class of constructible sets, leads to G6del's result that the axiom of choice and the continuum hypothesis are consistent with the rest of set theory [1]I. The text thus constitutes an introduction to the results of P. Cohen concerning the independence of these axioms [2], and to many other relative consistency proofs obtained later by Cohen's methods. Chapters I and II introduce the axioms of set theory, and develop such parts of the theory as are indispensable for every relative consistency proof; the method of recursive definition on the ordinals being an import ant case in point. Although, more or less deliberately, no proofs have been omitted, the development here will be found to require of the reader a certain facility in naive set theory and in the axiomatic method, such e as should be achieved, for example, in first year graduate work (2 cycle de mathernatiques).

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