Adversarial Barrier in Uniform Class Separation
By: Milan Rosko
Potential Business Impact:
Makes math proofs work better for computers.
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.
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