Adversarial Barrier in Uniform Class Separation
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912763901640704 |
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| author | Rosko, Milan |
| author_facet | Rosko, Milan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08149 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adversarial Barrier in Uniform Class Separation Rosko, Milan Logic Computational Complexity Logic in Computer Science 68Q15, 03F30, 03D20, 03F25, 03D25, F.1.0; F.2.0; F.4.1 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. |
| title | Adversarial Barrier in Uniform Class Separation |
| topic | Logic Computational Complexity Logic in Computer Science 68Q15, 03F30, 03D20, 03F25, 03D25, F.1.0; F.2.0; F.4.1 |
| url | https://arxiv.org/abs/2512.08149 |