A program for the full axiom of choiceArticle
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Jean-Louis Krivine
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.
Volume: Volume 17, Issue 3
Published on: September 1, 2021
Accepted on: June 30, 2021
Submitted on: June 11, 2020
Keywords: Computer Science - Logic in Computer Science, Mathematics - Logic, 03E40, F.4.1