Gaisi Takeuti

Proof Theory (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

Produktdetails

• Verlag: Dover Publications
• Erscheinungstermin: 10. Oktober 2013
• Englisch
• ISBN-13: 9780486320670
• Artikelnr.: 44196091

Inhaltsangabe

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