LIPIcs.TYPES.2013.24.pdf
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A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle
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19th International Conference on Types for Proofs and Programs (TYPES 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Types for Proofs and Programs (TYPES) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2014-07-25
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Federico Aschieri and Margherita Zorzi. A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 24-44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.TYPES.2013.24
https://doi.org/10.4230/LIPIcs.TYPES.2013.24
Abstract
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 functional language, which is Goedel's System T enriched with some syntactic sugar.
Keywords
- Markov's Principle
- Intuitionistic Realizability
- Heyting Arithmetic
- Game Semantics
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