Schindler Ways of Proof Theory

1. Auflage 2013
ISBN: 978-3-11-032490-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 2, 498 Seiten

Reihe: Ontos Mathematical LogicISSN

On the occasion of the retirement of Wolfram Pohlers the Institut für Mathematische Logik und Grundlagenforschung of the University of Münster organized a colloquium and a workshop which took place July 17 – 19, 2008. This event brought together proof theorists from many parts of the world who have been acting as teachers, students and collaborators of Wolfram Pohlers and who have been shaping the field of proof theory over the years. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.

Autoren/Hrsg.

Schindler, Ralf

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;Wolfram Pohlers—Life and Work;9
4;The Proof Theory of Classical and Constructive Inductive Definitions. A Forty Year Saga, 1968 – 2008;15
5;A New Approach to Predicative Set Theory;39
6;Characterising Definable Search Problems inBounded Arithmetic via Proof Notations;73
7;On Topological Models of GLP;143
8;Program Extraction via Typed Realisability for Induction and Coinduction;165
9;Another Reduction of Classical ID. to Constructive IDi.;191
10;Elementary Constructive Operational Set Theory;207
11;Functional Interpretations of Classical Systems;249
12;Towards a Formal Theory of Computability;265
13;S11Choice in a Theory of Sets and Classes;291
14;An Extended Predicative Definition of the Mahlo Universe;323
15;ITTMs with Feedback;349
16;Logspace without Bounds;363
17;Investigations of Subsystems of Second Order Arithmetic and Set Theory in Strength between .11-CA and .12-CA + BI: Part I;371
18;Weak Theories of Operations and Types;449
19;Computing Bounds from Arithmetical Proofs;477

Über Autor(innen)

Ralf Schindler studied Philosophy in Munich and did his Ph.D. in mathematics in Bonn. He held PostDoc positions in Berkeley and Vienna. Since 2003 he has been a professor for mathematical logic at the university of Münster.