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.
Contrapositive of countable choice · Double negation elimination · Heyting arithmetic · Elementary analysis · Recursive · Decidable · Church’s thesis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/927871
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