This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. The chapters are carefully organized, featuring complete proofs and numerous ...
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This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as G???del's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindstr???m's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.
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Add this copy of Mathematical Logic: Undergraduate Texts in Mathematics to cart. $13.11, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1984 by Springer-Verlag.
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Add this copy of Mathematical Logic: Undergraduate Texts in Mathematics to cart. $15.00, very good condition, Sold by A Cappella Books rated 5.0 out of 5 stars, ships from Atlanta, GA, UNITED STATES, published 1990 by Springer-Verlag.
Add this copy of Mathematical Logic (Undergraduate Texts in Mathematics) to cart. $24.00, very good condition, Sold by Row by Row Bookshop rated 5.0 out of 5 stars, ships from Sugar Grove, NC, UNITED STATES, published 1984 by Springer-Verlag.
Add this copy of Mathematical Logic to cart. $24.95, very good condition, Sold by Mahler Books rated 5.0 out of 5 stars, ships from Pflugerville, TX, UNITED STATES, published 1985 by Springer.
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Very Good. 0387961704. This book is in very good condition; no remainder marks. It does have some cover shelfwear. Inside pages are clean.; Undergraduate Texts In Mathematics; 225 pages.
Add this copy of Mathematical Logic to cart. $30.00, like new condition, Sold by Midway Book Store rated 4.0 out of 5 stars, ships from Saint Paul, MN, UNITED STATES, published 1984 by Springer.
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Fine. 24.5 x 16 cm. 216pp. Bound into glossy yellow boards. Undergraduate Texts in Mathematics. Junior/senior level text devoted to a study of first-order logic and its role in the foundations of mathematics.
Add this copy of Mathematical Logic to cart. $30.95, very good condition, Sold by Daedalus Books rated 4.0 out of 5 stars, ships from Portland, OR, UNITED STATES, published 1994 by Springer.
