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A first-order completeness result about characteristic Boolean algebras in classical realizability

09/19/2022

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by Guillaume Geoffroy, et al.

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We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily equivalent to it. This is done by controlling precisely which combinations of so-called "angelic" (or "may") and "demonic" (or "must") nondeterminism exist in the underlying model of computation.

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