Proof Theory - Brossura

Takeuti, Gaisi

Brossura

ISBN 10: 0486490734 ISBN 13: 9780486490731

Casa editrice: Dover Pubns, 2013

Riassunto

Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics.
The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.

Su questo libro

Recensione:

This comprehensive monograph
is a cornerstone in the area of
mathematical logic and related
fields. Focusing on Gentzen-type
proof theory, the book presents a
detailed overview of creative works by the author and other
20th-century logicians that includes applications of proof
theory to logic as well as other areas of mathematics.
Reprint of the North Holland, Amsterdam, 1987 edition.

Contenuti:

Preface Preface to the Second Edition Contents Introduction Part I. First Order Systems 1. First Order Predicate Calculus 2. Peano Arithmetic Part II. Second Order and Finite Order Systems 3. Second Order Systems and Simple Type Theory 4. Infinitary Logic Part III. Consistency Problems 5. Consistency Proofs 6. Some Applications of Consistency Proofs Postscript Appendix Index

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2013
• ISBN 10: 0486490734
• ISBN 13: 9780486490731
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 490