Berger / Diener / Schuster Logic, Construction, Computation

1. Auflage 2013
ISBN: 978-3-11-032492-1
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 3, 542 Seiten

Reihe: Ontos Mathematical LogicISSN

Over the last few decades the interest of logicians and mathematicians in constructive and computational aspects of their subjects has been steadily growing, and researchers from disparate areas realized that they can benefit enormously from the mutual exchange of techniques concerned with those aspects. A key figure in this exciting development is the logician and mathematician Helmut Schwichtenberg to whom this volume is dedicated on the occasion of his 70th birthday and his turning emeritus. The volume contains 20 articles from leading experts about recent developments in Constructive set theory, Provably recursive functions, Program extraction, Theories of truth, Constructive mathematics, Classical vs. intuitionistic logic, Inductive definitions, and Continuous functionals and domains.

Autoren/Hrsg.

Berger, Ulrich

Diener, Hannes

Schuster, Peter

Seisenberger, Monika

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;Contributors;11
4;A New Use of Friedman’s Translation: Interactive Realizability;15
5;Polymorphic Logic;55
6;Constructive Solutions of Ordinary Differential Equations;71
7;A Nonstandard Hierarchy Comparison Theorem for the Slow and Fast Growing Hierarchy;83
8;Conservativity of transitive closure over weak constructive operational set theory. Dedicated to Prof. Helmut Schwichtenberg;95
9;Formal Baire Space in Constructive Set Theory;127
10;Functional Interpretations of Classical and Constructive Set Theory;141
11;Weak Theories of Truth and Explicit Mathematics. Dedicated to Helmut Schwichtenberg on his retirement;161
12;Axiomatizing Truth: Why and How? For Helmut Schwichtenberg on the occasion of his 70th birthday;189
13;On the Strength of some Semi-Constructive Theories;205
14;On the Relation Between Various Negative Translations;231
15;A Finite Axiomatisation of Inductive-Inductive Definitions;263
16;Some Conservative Extension Results on Classical and Intuitionistic Sequent Calculi;293
17;About the Strength of Operational Regularity. Dedicated to Helmut Schwichtenberg on his retirement;309
18;Non-Deterministic Epsilon Substitution for ID1: Effective Proof;329
19;Another Unique Weak König’s Lemma WKL!! For Helmut Schwichtenberg, with respect and appreciation for his encouragement and friendship.;347
20;The Continuous Functionals as Limit Spaces;357
21;Provably Recursive Functions of Reflection;385
22;A Hierarchy of Ramified Theories Below PRA;479
23;Representing L-Domains as Information Systems;505