English

Adversarial Barrier in Uniform Class Separation

Logic 2025-12-16 v3 Computational Complexity Logic in Computer Science

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.

Keywords

Cite

@article{arxiv.2512.08149,
  title  = {Adversarial Barrier in Uniform Class Separation},
  author = {Milan Rosko},
  journal= {arXiv preprint arXiv:2512.08149},
  year   = {2025}
}

Comments

9 pages, 2 figures. A structural obstruction shows uniform separation in HA collapses into fixed-point paradoxes, independent of semantics

R2 v1 2026-07-01T08:15:57.120Z