An Introduction To Proof Theory: Normalization, Cut-elimination, And Consistency Proofs

September 16, 2021|
An Introduction To Proof Theory: Normalization, Cut-elimination, And Consistency Proofs by Paolo Mancosu
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An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader''s understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Godel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen''s consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach''s introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
Paolo Mancosu is Willis S. and Marion Slusser Professor of Philosophy at the University of California at Berkeley. He is the author of numerous articles and books in logic and philosophy of mathematics. During his career he has taught at Stanford, Oxford, and Yale. He was awarded a fellowship at the Wissenschaftskolleg zu Berlin in 199...
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Title:An Introduction To Proof Theory: Normalization, Cut-elimination, And Consistency Proofs
Format:Paperback
Product dimensions:432 pages, 9.21 X 6.14 X 0.07 in
Shipping dimensions:432 pages, 9.21 X 6.14 X 0.07 in
Published:September 16, 2021
Publisher:Oxford University Press
Language:English
Appropriate for ages:All ages
ISBN - 13:9780192895943

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