$\mathrm{P}\ne \mathrm{NP}$ and All Non-Empty Sets in $\mathrm{NP}\cup \mathrm{coNP}$ Have P-Optimal Proof Systems Relative to an Oracle

Abstract

As one step in a working program initiated by Pudlák [Pud17] we construct an oracle relative to which $\mathrm{P}\ne \mathrm{NP}$ and all non-empty sets in $\mathrm{NP}\cup \mathrm{coNP}$ have $\mathrm{P}$-optimal proof systems.

arXiv admin note: substantial text overlap with arXiv:1904.06175, arXiv:1903.11860, arXiv:1910.08571