Logic, Construction, Computation

Main 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 Preface Contents Contributors A New Use of Friedman’s Translation: Interactive Realizability Polymorphic Logic Constructive Solutions of Ordinary Differential Equations A Nonstandard Hierarchy Comparison Theorem for the Slow and Fast Growing Hierarchy Conservativity of transitive closure over weak constructive operational set theory. Dedicated to Prof. Helmut Schwichtenberg Formal Baire Space in Constructive Set Theory Functional Interpretations of Classical and Constructive Set Theory Weak Theories of Truth and Explicit Mathematics. Dedicated to Helmut Schwichtenberg on his retirement Axiomatizing Truth: Why and How? For Helmut Schwichtenberg on the occasion of his 70th birthday On the Strength of some Semi-Constructive Theories On the Relation Between Various Negative Translations A Finite Axiomatisation of Inductive-Inductive Definitions Some Conservative Extension Results on Classical and Intuitionistic Sequent Calculi About the Strength of Operational Regularity. Dedicated to Helmut Schwichtenberg on his retirement Non-Deterministic Epsilon Substitution for ID1: Effective Proof Another Unique Weak König’s Lemma WKL!! For Helmut Schwichtenberg, with respect and appreciation for his encouragement and friendship. The Continuous Functionals as Limit Spaces Provably Recursive Functions of Reflection A Hierarchy of Ramified Theories Below PRA Representing L-Domains as Information Systems

In the last decades, mathematical logic has developed into a technically quite sophisticated area of mathematics. Nevertheless, inspirations from philosophy and computer science continue to be important and noticeable. The series publishes conference proceedings as well as monographs written by leading researchers in mathematical logic.