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On Constructive Interpretation of Predictive Mathematics (1990) de Charles Parsons

On Constructive Interpretation of Predictive Mathematics (1990)

Autor Charles Parsons
en Limba Engleză Paperback – 31 mai 2018
First published in 1990, this book consists of a detailed exposition of results of the theory of "interpretation" developed by G. Kreisel — the relative impenetrability of which gives the elucidation contained here great value for anyone seeking to understand his work. It contains more complex versions of the information obtained by Kreisel for number theory and clustering around the no-counter-example interpretation, for number-theorectic forumulae provide in ramified analysis. It also proves the omega-consistency of ramified analysis. The author also presents proofs of Schütte’s cut-elimination theorems which are based on his consistency proofs and essentially contain them — these went further than any published work up to that point, helping to squeeze the maximum amount of information from these proofs.
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Specificații

ISBN-13: 9781138226678
ISBN-10: 113822667X
Pagini: 360
Dimensiuni: 156 x 234 mm
Greutate: 0.54 kg
Ediția:1
Editura: Taylor & Francis
Colecția Routledge
Locul publicării:Oxford, United Kingdom

Cuprins

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

Descriere

First published in 1990, this book consists of a detailed exposition of results of the theory of "interpretation" developed by G. Kreisel — the relative impenetrability of which gives the elucidation contained here great value for anyone seeking to understand his work.