Foundations of Mathematical Logic

Author: Haskell Brooks Curry
Publisher: Courier Corporation
ISBN: 9780486634623
Category: Mathematics
Page: 408
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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

An Introductory Survey
Author: G. T. Kneebone
Publisher: Dover Publications
ISBN: 9780486417127
Category: Mathematics
Page: 435
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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.

Mathematical Logic

Author: Stephen Cole Kleene
Publisher: Courier Corporation
ISBN: 0486317072
Category: Mathematics
Page: 416
View: 7463

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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.

Introduction to the Foundations of Mathematics

Second Edition
Author: Raymond L. Wilder
Publisher: Courier Corporation
ISBN: 0486276201
Category: Mathematics
Page: 352
View: 5243

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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.

Logic for Mathematicians

Author: J. Barkley Rosser
Publisher: Courier Dover Publications
ISBN: 0486468984
Category: Mathematics
Page: 574
View: 8056

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Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use.

Undecidable Theories

Author: Alfred Tarski,Andrzej Mostowski,Raphael Mitchel Robinson
Publisher: Elsevier
ISBN: 0444533788
Category: Decidability (Mathematical logic)
Page: 98
View: 7309

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The Elements of Mathematical Logic

Author: Paul C. Rosenbloom
Publisher: Courier Corporation
ISBN: 0486446174
Category: Mathematics
Page: 214
View: 7617

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This introduction to mathematical logic stresses the use of logical methods in attacking nontrivial problems. It covers the logic of classes, of propositions, of propositional functions, and the general syntax of language, with a brief introduction to so-called undecidability and incompleteness theorems; and much more. 1950 edition.

Introduction to Logic

Author: Patrick Suppes
Publisher: Courier Corporation
ISBN: 0486138054
Category: Mathematics
Page: 336
View: 7334

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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.

Fundamentals of Mathematical Logic

Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Category: Mathematics
Page: 896
View: 1422

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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: 0486782972
Category: Mathematics
Page: 304
View: 5445

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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.

Foundations of Geometry

Author: C. R. Wylie
Publisher: Courier Corporation
ISBN: 0486472140
Category: Education
Page: 338
View: 2564

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Explains geometric theories and shows many examples.

Foundations and Fundamental Concepts of Mathematics

Author: Howard Eves
Publisher: Courier Corporation
ISBN: 048613220X
Category: Mathematics
Page: 368
View: 2583

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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.

First Course in Mathematical Logic

Author: Patrick Suppes,Shirley Hill
Publisher: Courier Corporation
ISBN: 0486150941
Category: Mathematics
Page: 288
View: 522

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Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.

Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition
Author: Jean H. Gallier
Publisher: Courier Dover Publications
ISBN: 0486805085
Category: Mathematics
Page: 528
View: 5467

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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.

The Continuum

A Critical Examination of the Foundation of Analysis
Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 0486679829
Category: Mathematics
Page: 130
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Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.

Principles of Mathematical Logic

Author: David Hilbert,Wilhelm Ackermann,Robert E. Luce
Publisher: American Mathematical Soc.
ISBN: 0821820249
Category: Mathematics
Page: 172
View: 6303

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David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. This translation is based on the second German edition and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Godel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.

A Profile of Mathematical Logic

Author: Howard DeLong
Publisher: Courier Corporation
ISBN: 0486139158
Category: Mathematics
Page: 320
View: 2035

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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.

First Order Mathematical Logic

Author: Angelo Margaris
Publisher: Courier Corporation
ISBN: 9780486662695
Category: Mathematics
Page: 211
View: 6665

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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


The Categorial Analysis of Logic
Author: Robert Goldblatt
Publisher: Courier Corporation
ISBN: 0486450260
Category: Mathematics
Page: 551
View: 7607

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A classic introduction to mathematical logic from the perspective of category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers. Its approach moves always from the particular to the general, following through the steps of the abstraction process until the abstract concept emerges naturally. Beginning with a survey of set theory and its role in mathematics, the text proceeds to definitions and examples of categories and explains the use of arrows in place of set-membership. The introduction to topos structure covers topos logic, algebra of subobjects, and intuitionism and its logic, advancing to the concept of functors, set concepts and validity, and elementary truth. Explorations of categorial set theory, local truth, and adjointness and quantifiers conclude with a study of logical geometry.

Set Theory and Logic

Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category: Mathematics
Page: 512
View: 2956

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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.