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Table of contents (8 chapters)
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Computability
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Provability and Computability
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About this book
Reviews
"As one might expect from a graduate text on logic by a very distinguished algebraic geometer, this book assumes no previous acquaintance with logic, but proceeds at a high level of mathematical sophistication. Chapters I and II form a short course. Chapter I is a very informal introduction to formal languages, e.g., those of first order Peano arithmetic and of ZFC set theory. Chapter II contains Tarski's definition of truth, Gödel's completeness theorem, and the Löwenheim-Skolem theorem. The emphasis is on semantics rather than syntax. Some rarely-covered side topics are included (unique readability for languages with parentheses, Mostowski's transitive collapse lemma, formalities of introducing definable constants and function symbols). Some standard topics are neglected. (The compactness theorem is not mentioned!) The latter part of Chapter II contains Smullyan's quick proof of Tarski's theorem on the undefinability of truth in formal arithmetic, and an account of the Kochen-Specker "no hidden variables" theorem in quantum logic. There are digressions on philosophical issues (formal logic vs. ordinary language, computer proofs). A wealth of material is introduced in these first 100 pages of the book..."--MATHEMATICAL REVIEWS
Authors and Affiliations
Bibliographic Information
Book Title: A Course in Mathematical Logic
Authors: Yu. I. Manin
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4757-4385-2
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1977
eBook ISBN: 978-1-4757-4385-2Published: 29 June 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XIII, 288