Set Theory and the Continuum Problem

Author: Raymond M. Smullyan
Publisher:
ISBN: 0486474844
Release Date: 2010
Genre: Mathematics

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.

Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 9780486469218
Release Date: 2008-12-09
Genre: Mathematics

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.

Basic Set Theory

Author: Azriel Levy
Publisher: Courier Corporation
ISBN: 9780486150734
Release Date: 2012-06-11
Genre: Mathematics

The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.

Zermelo s Axiom of Choice

Author: G.H. Moore
Publisher: Springer Science & Business Media
ISBN: 9781461394785
Release Date: 2012-12-06
Genre: Mathematics

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.

Axiomatic Set Theory

Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 9780486136875
Release Date: 2012-05-04
Genre: Mathematics

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: 9780486497082
Release Date: 2014-07-23
Genre: Mathematics

"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"--

The Philosophy of Set Theory

Author: Mary Tiles
Publisher: Courier Corporation
ISBN: 9780486138558
Release Date: 2012-03-08
Genre: Mathematics

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

Continuum Mechanics

Author: P. Chadwick
Publisher: Courier Corporation
ISBN: 9780486139142
Release Date: 2012-08-08
Genre: Science

DIVComprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. /div

Recursion Theory for Metamathematics

Author: Raymond M. Smullyan
Publisher: Oxford University Press
ISBN: 0195344812
Release Date: 1993-01-28
Genre: Mathematics

This work is a sequel to the author's G?del's Incompleteness Theorems, though it can be read independently by anyone familiar with G?del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

An Introduction to Stability Theory

Author: Anand Pillay
Publisher: Courier Corporation
ISBN: 9780486150437
Release Date: 2013-05-17
Genre: Mathematics

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.

Models and Ultraproducts

Author: John Lane Bell
Publisher: Courier Corporation
ISBN: 9780486449791
Release Date: 2006
Genre: Mathematics

In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.

Undecidable Theories

Author: Alfred Tarski
Publisher: Elsevier
ISBN: 9780444533784
Release Date: 1953
Genre: Decidability (Mathematical logic)


Incompleteness in the Land of Sets

Author: Melvin Fitting
Publisher:
ISBN: 1904987346
Release Date: 2007
Genre: Mathematics

Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of Godel, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. Godel numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to Godel's Second Incompleteness Theorem. Exercises are scattered throughout.

Philosophical Introduction to Set Theory

Author: Stephen Pollard
Publisher: Courier Dover Publications
ISBN: 9780486797144
Release Date: 2015-07-15
Genre: Mathematics

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.