Axiomatic Set Theory

2012-05-04 Mathematics

Author : Patrick Suppes
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.

Axiomatic Set Theory

2013-12-01 Mathematics

Author : G. Takeuti
Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 515/5 ( reviews)

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Book Synopsis Axiomatic Set Theory by : G. Takeuti

Download or read book Axiomatic Set Theory written by G. Takeuti. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained.

Introduction to Axiomatic Set Theory

2012-12-06 Mathematics

Author : G. Takeuti
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.

The Foundations of Mathematics

2009 Mathematics

Author : Kenneth Kunen
Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 147/5 ( reviews)

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Book Synopsis The Foundations of Mathematics by : Kenneth Kunen

Download or read book The Foundations of Mathematics written by Kenneth Kunen. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Set Theory

1983

Author : Kenneth Kunen
Release : 1983
Genre :
Kind : eBook
Book Rating : 009/5 ( reviews)

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Book Synopsis Set Theory by : Kenneth Kunen

Download or read book Set Theory written by Kenneth Kunen. This book was released on 1983. Available in PDF, EPUB and Kindle. Book excerpt:

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