The extensional realizability model of continuous functionals and three weakly non-constructive classical theorems

Abstract

We investigate wether three statements in analysis, that can be provedclassically, are realizable in the realizability model of extensionalcontinuous functionals induced by Kleene's second model $K_2$. We prove that aformulation of the Riemann Permutation Theorem as well as the statement thatall partially Cauchy sequences are Cauchy cannot be realized in this model,while the statement that the product of two anti-Specker spaces is anti-Speckercan be realized