Almost sure OTM-realizability differs from plain realizability but remains closed under intuitionistic predicate logic and realizes Kripke-Platek set theory.
Otherwise, by definition of as-OTM-realizability for formulas with free variables, an as-OTM- realizer for ϕ → ψ(a) is one for ∀a(ϕ → ψ(a))
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Almost sure OTM-realizability
Almost sure OTM-realizability differs from plain realizability but remains closed under intuitionistic predicate logic and realizes Kripke-Platek set theory.