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  1. Bog
  2. Emner i filosofi
  3. Filosofi: logik

An Introduction to Proof Theory

- Normalization, Cut-Elimination, and Consistency Proofs
Af: Sergio Galvan, Richard Zach, Paolo Mancosu Engelsk Paperback

An Introduction to Proof Theory

- Normalization, Cut-Elimination, and Consistency Proofs
Af: Sergio Galvan, Richard Zach, Paolo Mancosu Engelsk Paperback
Tjek vores konkurrenters priser
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.
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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 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.
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Produktdetaljer
Sprog: Engelsk
Sider: 432
ISBN-13: 9780192895943
Indbinding: Paperback
Udgave:
ISBN-10: 019289594X
Kategori: Filosofi: logik
Udg. Dato: 17 aug 2021
Længde: 26mm
Bredde: 233mm
Højde: 157mm
Forlag: Oxford University Press
Oplagsdato: 17 aug 2021
Forfatter(e): Sergio Galvan, Richard Zach, Paolo Mancosu
Forfatter(e) Sergio Galvan, Richard Zach, Paolo Mancosu

Kategori Filosofi: logik

ISBN-13 9780192895943

Sprog Engelsk

Indbinding Paperback

Sider 432

Udgave

Længde 26mm

Bredde 233mm

Højde 157mm

Udg. Dato 17 aug 2021

Oplagsdato 17 aug 2021

Forlag Oxford University Press

Kategori sammenhænge