A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle

Federico Aschieri, Margherita Zorzi, Marc Herbstritt
2014 Types for Proofs and Programs  
We propose a very simple modification of Kreisel's modified realizability in order to computationally realize Markov's Principle in the context of Heyting Arithmetic. Intuitively, realizers correspond to arbitrary strategies in Hintikka-Tarski games, while in Kreisel's realizability they can only represent winning strategies. Our definition, however, does not employ directly game semantical concepts and remains in the style of functional interpretations. As term calculus, we employ a purely
more » ... tional language, which is Gödel's System T enriched with some syntactic sugar.
doi:10.4230/lipics.types.2013.24 dblp:conf/types/AschieriZ13 fatcat:wtplkohcbvg3xhtktcioemcvyu