Foundations of Mathematical Logic

Author: Haskell Brooks Curry
Publisher: Courier Corporation
ISBN: 0486634620
Release Date: 1963
Genre: Mathematics

Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.

Mathematical Logic and the Foundations of Mathematics

Author: G. T. Kneebone
Publisher: Dover Publications
ISBN: 0486417123
Release Date: 2001
Genre: Mathematics

Ideal for students intending to specialize in the topic. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics. Part III focuses on the philosophy of mathematics.

Handbook of Mathematical Logic

Author: J. Barwise
Publisher: Elsevier
ISBN: 0080933645
Release Date: 1982-03-01
Genre: Mathematics

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

Mathematical Logic

Author: Stephen Cole Kleene
Publisher: Courier Corporation
ISBN: 9780486317076
Release Date: 2013-04-22
Genre: Mathematics

Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Fundamentals of Mathematical Logic

Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 9781439864272
Release Date: 2018-10-08
Genre: Mathematics

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

A Beginner s Guide to Mathematical Logic

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 9780486782973
Release Date: 2014-03-19
Genre: Mathematics

Combining stories of great writers and philosophers with quotations and riddles, this completely original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2013 edition.

Introduction to Logic

Author: Alfred Tarski
Publisher: Courier Corporation
ISBN: 9780486318899
Release Date: 2013-07-04
Genre: Mathematics

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

Introduction to Logic

Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 9780486138053
Release Date: 2012-07-12
Genre: Mathematics

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.

A Profile of Mathematical Logic

Author: Howard DeLong
Publisher: Courier Corporation
ISBN: 9780486139159
Release Date: 2012-09-26
Genre: Mathematics

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.

Logic for Computer Science

Author: Jean H. Gallier
Publisher: Courier Dover Publications
ISBN: 9780486780825
Release Date: 2015-06-18
Genre: Computers

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

Introduction to the Foundations of Mathematics

Author: Raymond L. Wilder
Publisher: Courier Corporation
ISBN: 9780486276205
Release Date: 2013-09-26
Genre: Mathematics

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

What Is Mathematical Logic

Author: J. N. Crossley
Publisher: Courier Corporation
ISBN: 9780486151526
Release Date: 2012-08-29
Genre: Mathematics

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.

An Introduction to Mathematical Logic

Author: Richard E. Hodel
Publisher: Courier Corporation
ISBN: 9780486497853
Release Date: 2013
Genre: Mathematics

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.

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.

Foundations and Fundamental Concepts of Mathematics

Author: Howard Eves
Publisher: Courier Corporation
ISBN: 9780486132204
Release Date: 2012-04-10
Genre: Mathematics

Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.