Proof Theory (Dover Books on Mathematics) (Paperback)

Proof Theory (Dover Books on Mathematics) By Gaisi Takeuti Cover Image
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Description


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 G del'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.


Product Details
ISBN: 9780486490731
ISBN-10: 0486490734
Publisher: Dover Publications
Publication Date: February 20th, 2013
Pages: 512
Language: English
Series: Dover Books on Mathematics