Logic, Construction, Computation (eBook)

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