A program for the full axiom of choice

Jean-Louis Krivine (1)

1 PPS - Preuves, Programmes et Systèmes

The theory of classical realizability is a framework for the Curry-Howard correspondence which enables to associate a program with each proof in Zermelo-Fraenkel set theory. But, almost all the applications of mathematics in physics, probability, statistics, etc. use Analysis i.e. the axiom of dependent choice (DC) or even the (full) axiom of choice (AC). It is therefore important to find explicit programs for these axioms. Various solutions have been found for DC, for instance the lambda-term called "bar recursion" or the instruction "quote" of LISP. We present here the first program for AC.

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

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Jean-Louis Krivine. A program for the full axiom of choice. Logical Methods in Computer Science, 2021, 17 (3), pp. 21:1-21:22. ⟨hal-02859846v3⟩