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

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