Abstract:In this paper we propose a new approach to realizability interpretations for
nonstandard arithmetic. We deal with nonstandard analysis in the context of
(semi)intuitionistic realizability, focusing on the Lightstone-Robinson
construction of a model for nonstandard analysis through an ultrapower. In
particular, we consider an extension of the $\lambda$-calculus with a memory
cell, that contains an integer (the state), in order to indicate in which slice
of the ultrapower $\cal{M}^{\mathbb{N}}$ the computation i… Show more
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