**Author**: Haskell Brooks Curry

**Publisher:**Courier Corporation

**ISBN:**9780486634623

**Category:**Mathematics

**Page:**408

**View:**5272

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# Search Results for: foundations-of-mathematical-logic-dover-books-on-mathematics

**Author**: Haskell Brooks Curry

**Publisher:** Courier Corporation

**ISBN:** 9780486634623

**Category:** Mathematics

**Page:** 408

**View:** 5272

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.
*An Introductory Survey*

**Author**: G. T. Kneebone

**Publisher:** Dover Publications

**ISBN:** 9780486417127

**Category:** Mathematics

**Page:** 435

**View:** 5572

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.

**Author**: Stephen Cole Kleene

**Publisher:** Courier Corporation

**ISBN:** 0486317072

**Category:** Mathematics

**Page:** 416

**View:** 7463

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.
*Second Edition*

**Author**: Raymond L. Wilder

**Publisher:** Courier Corporation

**ISBN:** 0486276201

**Category:** Mathematics

**Page:** 352

**View:** 5243

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.

**Author**: J. Barkley Rosser

**Publisher:** Courier Dover Publications

**ISBN:** 0486468984

**Category:** Mathematics

**Page:** 574

**View:** 8056

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.

**Author**: Alfred Tarski,Andrzej Mostowski,Raphael Mitchel Robinson

**Publisher:** Elsevier

**ISBN:** 0444533788

**Category:** Decidability (Mathematical logic)

**Page:** 98

**View:** 7309

**Author**: Paul C. Rosenbloom

**Publisher:** Courier Corporation

**ISBN:** 0486446174

**Category:** Mathematics

**Page:** 214

**View:** 7617

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.

**Author**: Patrick Suppes

**Publisher:** Courier Corporation

**ISBN:** 0486138054

**Category:** Mathematics

**Page:** 336

**View:** 7334

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.

**Author**: Peter G. Hinman

**Publisher:** CRC Press

**ISBN:** 1439864276

**Category:** Mathematics

**Page:** 896

**View:** 1422

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.

**Author**: Raymond M. Smullyan

**Publisher:** Courier Corporation

**ISBN:** 0486782972

**Category:** Mathematics

**Page:** 304

**View:** 5445

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.

**Author**: C. R. Wylie

**Publisher:** Courier Corporation

**ISBN:** 0486472140

**Category:** Education

**Page:** 338

**View:** 2564

Explains geometric theories and shows many examples.

**Author**: Howard Eves

**Publisher:** Courier Corporation

**ISBN:** 048613220X

**Category:** Mathematics

**Page:** 368

**View:** 2583

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.

**Author**: Patrick Suppes,Shirley Hill

**Publisher:** Courier Corporation

**ISBN:** 0486150941

**Category:** Mathematics

**Page:** 288

**View:** 522

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.
*Foundations of Automatic Theorem Proving, Second Edition*

**Author**: Jean H. Gallier

**Publisher:** Courier Dover Publications

**ISBN:** 0486805085

**Category:** Mathematics

**Page:** 528

**View:** 5467

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.
*A Critical Examination of the Foundation of Analysis*

**Author**: Hermann Weyl

**Publisher:** Courier Corporation

**ISBN:** 0486679829

**Category:** Mathematics

**Page:** 130

**View:** 9430

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.

**Author**: David Hilbert,Wilhelm Ackermann,Robert E. Luce

**Publisher:** American Mathematical Soc.

**ISBN:** 0821820249

**Category:** Mathematics

**Page:** 172

**View:** 6303

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.

**Author**: Howard DeLong

**Publisher:** Courier Corporation

**ISBN:** 0486139158

**Category:** Mathematics

**Page:** 320

**View:** 2035

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.

**Author**: Angelo Margaris

**Publisher:** Courier Corporation

**ISBN:** 9780486662695

**Category:** Mathematics

**Page:** 211

**View:** 6665

"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

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.

**Author**: Robert R. Stoll

**Publisher:** Courier Corporation

**ISBN:** 0486139646

**Category:** Mathematics

**Page:** 512

**View:** 2956

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.

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