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