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Where is the Gödel-point hiding: Gentzen’s Consistency Proof of 1936 and His Representation of Constructive Ordinals

Part of the SpringerBriefs in Philosophy Book Series

DOI: 10.1007/978-3-319-02171-3

ISBN: 978-3-319-02170-6

Publisher: Springer International Publishing - Springer Journals

Oct 23, 2013

1 - 4 of 4 Chapters

LitStream

Chapter 1Introduction

Horská, Anna

Pages: 1 –9

[This chapter deals with brief history of Gentzen’s consistency proofs and his work on proof systems which were actually byproducts of his ambition to prove the consistency of arithmetic. There is a plan in his handwritten thesis manuscript according to which he aimed to prove the consistency...
LitStream

Chapter 2Preliminaries

Horská, Anna

Pages: 11 –28

[The calculus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Chapter 3Ordinal Numbers

Horská, Anna

Pages: 29 –40

[Gentzen’s representation of ordinal numbers less than ε0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 4Consistency Proof

Horská, Anna

Pages: 41 –69

[Gentzen’s consistency proof of 1936 is explained in full detail. The chapter begins with the method of assigning ordinal numbers in Gentzen’s representation to derivations. The second part introduces reduction steps for derivations whose endsequent is not in endform and shows, at the same time,...

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