$\mathrm{P}$-Optimal Proof Systems for Each $\mathrm{coNP}$-Complete Set and no Complete Problems in $\mathrm{NP}\cap\mathrm{coNP}$ Relative to an Oracle
Titus Dose · arXiv (Cornell University) · 2019
We build on a working program initiated by Pudlák [Pud17] and construct an oracle relative to which each $\mathrm{coNP}$-complete set has $\mathrm{P}$-optimal proof systems and $\mathrm{NP}\cap\mathrm{coNP}$ does not have complete problems.