We show that in elementary analysis (EL) the contrapositive of countable choice is equivalent to double negation elimination for 2 0 -formulas. By also proving a recursive adaptation of this equivalence in Heyting arithmetic (HA), we give an instance of the conservativity of EL over HA with respect to recursive functions and predicates. As a complement, we prove in HA enriched with the (extended) Church thesis that every decidable predicate is recursive.
On the contrapositive of countable choice
Schuster, Peter Michael
2011-01-01
Abstract
We show that in elementary analysis (EL) the contrapositive of countable choice is equivalent to double negation elimination for 2 0 -formulas. By also proving a recursive adaptation of this equivalence in Heyting arithmetic (HA), we give an instance of the conservativity of EL over HA with respect to recursive functions and predicates. As a complement, we prove in HA enriched with the (extended) Church thesis that every decidable predicate is recursive.
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