Randomising Realisability

We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of randomly realisable statements is closed under intuitioni...

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Published in:arXiv.org 2021-01
Main Authors: Merlin, Carl, Galeotti, Lorenzo, Passmann, Robert
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Language:English
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Arithmetic
Axioms
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Galeotti, Lorenzo
Passmann, Robert
description We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of randomly realisable statements is closed under intuitionistic first-order logic, but (ii) different from the set of realisable statements, that (iii) "realisability with probability 1" is the same as realisability and (iv) that the axioms of bounded Heyting's arithmetic are randomly realisable, but some instances of the full induction scheme fail to be randomly realisable.
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subjects Arithmetic
Axioms
title Randomising Realisability
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