Realizability algebras: a program to well order R

Jean-Louis Krivine (1)

1 PPS - Preuves, Programmes et Systèmes

We give a method to transform into programs, classical proofs using a well ordering of the reals. The technology uses a generalization of Cohen's forcing and the theory of classical realizability introduced by the author.

Mots clés: Curry-Howard correspondence; combinatory logic; lambda-calculus; axiom of choice

Domaines: Logique en informatique [cs.LO]

Jean-Louis Krivine. Realizability algebras: a program to well order R. Logical Methods in Computer Science, 2011, 7 (3), pp.1-47. ⟨hal-00483232v2⟩