Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 0486469212
Format: PDF, Kindle
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This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Set Theory and the Continuum Problem

Author: Raymond M. Smullyan
Publisher:
ISBN: 9780486474847
Format: PDF, ePub, Docs
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A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

Zermelo s Axiom of Choice

Author: G.H. Moore
Publisher: Springer Science & Business Media
ISBN: 1461394783
Format: PDF, Mobi
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This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.

The Philosophy of Set Theory

Author: Mary Tiles
Publisher: Courier Corporation
ISBN: 0486138550
Format: PDF
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DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

Axiomatic Set Theory

Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486136876
Format: PDF
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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.

A Book of Set Theory

Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486497089
Format: PDF, Mobi
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"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

An Introduction to Stability Theory

Author: Anand Pillay
Publisher: Courier Corporation
ISBN: 0486150437
Format: PDF, Docs
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This introductory treatment covers the basic concepts and machinery of stability theory. Full of examples, theorems, propositions, and problems, it is suitable for graduate students, professional mathematicians, and computer scientists. 1983 edition.

Philosophical Introduction to Set Theory

Author: Stephen Pollard
Publisher: Courier Dover Publications
ISBN: 0486805824
Format: PDF, ePub, Docs
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The primary mechanism for ideological and theoretical unification in modern mathematics, set theory forms an essential element of any comprehensive treatment of the philosophy of mathematics. This unique approach to set theory offers a technically informed discussion that covers a variety of philosophical issues. Rather than focusing on intuitionist and constructive alternatives to the Cantorian/Zermelian tradition, the author examines the two most important aspects of the current philosophy of mathematics, mathematical structuralism and mathematical applications of plural reference and plural quantification. Clearly written and frequently cited in the mathematical literature, this book is geared toward advanced undergraduates and graduate students of mathematics with some aptitude for mathematical reasoning and prior exposure to symbolic logic. Suitable as a source of supplementary readings in a course on set theory, it also functions as a primary text in a course on the philosophy of mathematics.