Abstract

Using a technique developed by Coquand and Hofmann [3] we verify that adding the analytical form MP1: $\forall \alpha (\neg \neg \exists {\rm{x}}\alpha ({\rm{x}}) = 0 \to \exists {\rm{x}}\alpha ({\rm{x}}) = 0)$ of Markov’s Principle does not increase the class of ${\rm{\Pi }}_2^0$ formulas provable in Kleene and Vesley’s formal system for intuitionistic analysis, or in subsystems obtained by omitting or restricting various axiom schemas in specified ways.