REALIZING REALIZABILITY RESULTS WITH CLASSICAL CONSTRUCTIONS

Quantitative classical realizability

Introduced by Dal Lago and Hofmann, quantitative realizability is a technique used to define models for logics based on Multiplicative Linear Logic. A particularity is that functions are interpreted as bounded time computable functions. It has been used to give new and uniform proofs of soundness of several type systems with respect to certain time complexity classes. We propose a reformulation...

Verificationism and classical realizability

This paper investigates the question of whether Krivine’s classical realizability can provide a verificationist interpretation of classical logic. We argue that this kind of realizability can be considered an adequate candidate for this semantic role, provided that the notion of verification involved is no longer based on proofs, but on programs. On this basis, we show that a special reading of...

Realizability in classical logic

The essential aim is to explore the Curry-Howard correspondence : we want to associate a program with each mathematical proof and to consider each theorem as a specification, i.e. to find the common behavior of the programs associated with every proof of this theorem. It is a very difficult and very interesting problem, which I call the ‘‘ specification problem ’’ in what follows. In the first ...

On Forcing and Classical Realizability

Variations on Realizability: Realizing the Propositional Axiom of Choice

Early investigators of realizability were interested in metamathematical questions. In keeping with the traditions of the time they concentrated on interpretations of one formal system in another. They considered an ad hoc collection of increasingly ingenious interpretations to establish consistency, independence and conservativity results. van Oosten’s contribution to the Workshop (see van Oos...