Adversarial Barrier in Uniform Class Separation

Abstract

We identify a strong structural obstruction to Uniform Separation in constructive arithmetic. The mechanism is independent of semantic content; it emerges whenever two distinct evaluator predicates are sustained in parallel and inference remains uniformly representable in an extension of HA. Under these conditions, any putative Uniform Class Separation principle becomes a distinguished instance of a fixed point construction. The resulting limitation is stricter in scope than classical separation barriers (Baker; Rudich; Aaronson et al.) insofar as it constrains the logical form of uniform separation within HA, rather than limiting particular relativizing, naturalizing, or algebrizing techniques.