Arithmetic complexity of the predicate logics of certain complete arithmetic theories Original Research Article

It is proved in this paper that the predicate logic of each complete constructive arithmetic theory T having the existential property is View the MathML source-complete. In this connection, the techniques of a uniform partial truth definition for intuitionistic arithmetic theories is used. The main theorem is applied to the characterization of the predicate logic corresponding to certain variant of the notion of realizable predicate formula. Namely, it is shown that the set of irrefutable predicate formulas is recursively isomorphic to the complement of the set ∅(ω+1). The notion of View the MathML source-realizability is defined on the basis of the notion of View the MathML source-function. It is proved that the predicate logic of View the MathML source-realizability is View the MathML source-hard.