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Author:   Charles Parsons
Publisher:   Taylor & Francis Ltd
Imprint:   Routledge
Weight:   0.453kg
ISBN:  

9781138226524

ISBN 10:   1138226521
Pages:   342
Publication Date:   08 August 2016
Audience:   College/higher education ,  College/higher education ,  Postgraduate, Research & Scholarly ,  Tertiary & Higher Education
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Preface; Chapter I. Introduction; 1. Statement of the Problem 2. Systems Considered 3. Metamathematical Methods of Proof; Chapter II. Over-Simple Interpretations; 1. Trivial Interpretation 2. Failure of Interpretation by Recursive Satisfaction 3. Dependence of the Proof of the Verifiable Formula corresponding to a Theorem; Chapter III. Herbrand Interpretation; 1. The Concept of Herbrand Interpretation 2. Herbrand Interpretation of Elementary Number Theory without Induction 3. Properties of the Interpretation 4. Impossibility of an Herbrand Interpretation of Number Theory with Induction; Chapter IV. The No-Counter-Example Interpretation of Number Theory; 1. Non-constructive Considerations 2. No-Counter-Example Interpretation of Number Theory without Induction 3. No-Counter-Example Interpretation, 1*-Consistency, and External Consistency 4. Ordinal Recursive Functionals, 1*-Consistency of Number Theory with Induction 5. Representation of Ordinal Recursive Functionals in Elementary Number Theory; Chapter V. Ramified Analysis; 1. Description of Systems 2. Ramified Analysis without Induction 3. Recursive Well-orderings and Ordinal Recursive Functionals 4. Ramified Analysis with Induction 5. Representation of Ordinal Recursive Functionals in Ramified Analysis; Chapter VI. Ω-Consistency; 1. Critique of the Concept of ω-Consistency 2. Ω-Consistency, External Consistency, and 1*-Consistency 3. Ω-Consistency of Ramified Analysis; Appendix I. Arithmetization of Schütte’s Cut-elimination theorems; Appendix II. Ordinal Functions; Bibliography; Index of Definitions

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