A Course in Mathematical Logic (Graduate Texts in Mathematics)

Manin, Yu.I.

ISBN 10: 0387902430 / ISBN 13: 9780387902432

Editore: Springer, 1977

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Covers are dirty. Blemishes and discoloration to boards. Bump to lower spine end and upper corners. No names, underlining, notes or highlighting. p3.

Codice articolo ABE-1775085021797

Dati bibliografici

• Titolo: A Course in Mathematical Logic (Graduate Texts in Mathematics)
• Editore: Springer
• Data di pubblicazione: 1977
• Lingua: Inglese
• ISBN 10: 0387902430
• ISBN 13: 9780387902432
• Rilegatura: Rilegato
• Edizione: prima edizione
• Condizione: discreto
• Dimensioni: 1,91 L x 15,88 A x 24,13 P centimetri 1,91 centimetri di larghezza per 15,88 centimetri di altezza per 24,13 centimetri di profondità
• Peso: 635 grammi

Descrizione articolo

Riassunto

This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a sub-class of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities.

Recensione

"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