An Introduction to Proof Theory is popular PDF and ePub book, written by Paolo Mancosu in 2021, it is a fantastic choice for those who relish reading online the Philosophy genre. Let's immerse ourselves in this engaging Philosophy book by exploring the summary and details provided below. Remember, An Introduction to Proof Theory can be Read Online from any device for your convenience.
An Introduction to Proof Theory Book PDF Summary
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 Gödel-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.
Detail Book of An Introduction to Proof Theory PDF
- Author : Paolo Mancosu
- Release : 30 September 2024
- Publisher : Oxford University Press
- ISBN : 9780192895936
- Genre : Philosophy
- Total Page : 431 pages
- Language : English
- PDF File Size : 19,7 Mb
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