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Set Theory and Logic

Set Theory and Logic Author Robert R. Stoll
ISBN-10 9780486139647
Release 2012-05-23
Pages 512
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Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.



Axiomatic Set Theory

Axiomatic Set Theory Author Patrick Suppes
ISBN-10 9780486136875
Release 2012-05-04
Pages 265
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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.



First Order Mathematical Logic

First Order Mathematical Logic Author Angelo Margaris
ISBN-10 0486662691
Release 1990
Pages 211
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"Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews



Naive Set Theory

Naive Set Theory Author Paul R. Halmos
ISBN-10 9780486814872
Release 2017-04-19
Pages 112
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Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.



Set Theory and the Continuum Hypothesis

Set Theory and the Continuum Hypothesis Author Paul J. Cohen
ISBN-10 9780486469218
Release 2008-12-09
Pages 154
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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.



Introduction to Logic

Introduction to Logic Author Patrick Suppes
ISBN-10 9780486138053
Release 2012-07-12
Pages 336
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Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.



Mathematical Logic

Mathematical Logic Author Joel W. Robbin
ISBN-10 9780486450186
Release 2006-07-07
Pages 238
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This self-contained text will appeal to readers from diverse fields and varying backgrounds. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition.



A Profile of Mathematical Logic

A Profile of Mathematical Logic Author Howard DeLong
ISBN-10 9780486139159
Release 2012-09-26
Pages 320
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This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.



The Philosophy of Set Theory

The Philosophy of Set Theory Author Mary Tiles
ISBN-10 9780486138558
Release 2012-03-08
Pages 256
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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



First order Logic

First order Logic Author Raymond M. Smullyan
ISBN-10 0486683702
Release 1995
Pages 158
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Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.



Philosophical Introduction to Set Theory

Philosophical Introduction to Set Theory Author Stephen Pollard
ISBN-10 9780486805825
Release 2015-07-20
Pages 192
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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.



An Introduction to Mathematical Logic

An Introduction to Mathematical Logic Author Richard E. Hodel
ISBN-10 9780486497853
Release 2013
Pages 491
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This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.



Popular Lectures on Mathematical Logic

Popular Lectures on Mathematical Logic Author Hao Wang
ISBN-10 9780486171043
Release 2014-09-22
Pages 292
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Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.



Toposes and Local Set Theories

Toposes and Local Set Theories Author John L. Bell
ISBN-10 9780486462868
Release 2008-01
Pages 267
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This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.



What Is Mathematical Logic

What Is Mathematical Logic Author J. N. Crossley
ISBN-10 9780486151526
Release 2012-08-29
Pages 96
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A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.



Topoi

Topoi Author Robert Goldblatt
ISBN-10 9780486317960
Release 2013-07-25
Pages 576
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A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers.



Basic Concepts of Mathematics and Logic

Basic Concepts of Mathematics and Logic Author Michael C. Gemignani
ISBN-10 9780486435060
Release 2004
Pages 280
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This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.