2 problems

0 votes0 replies0 views
The Ω-recursive theory conjecture under supercompact cardinals
Assume that there exists a proper class of supercompact cardinals. Let $T$ be the set of all $\Sigma^2_2$ sentences $\phi$ such that $V\vDash\phi$ . A set of sentences is Ω-recursiv…
Conjectureopenlarge-cardinals omega-logic set-theoryarXiv posted 2 days ago
0 votes0 replies0 views
Woodin's equivalence between the Ω conjecture and Ω-provable closure
Assume there is a proper class of Woodin cardinals. A formula $(\exists x)\,\varphi(x)$ is a large cardinal axiom when $\varphi(x)$ is a $\Sigma_2$ formula and ZFC proves that ever…
Theoremopenlarge-cardinals omega-logic set-theoryarXiv posted 2 days ago

The Ω-recursive theory conjecture under supercompact cardinals