What would be arithmetic hierarchy of the form of formula like $\phi \wedge \psi$ where $\phi$ is $\Sigma_1^0$ and $\psi$ is $\Pi_1^0$? Prenex normal form seems to give me no answer for this.
2026-03-29 15:02:27.1774796547
What would be arithmetic hierarchy of $\Sigma_1^0 \wedge \Pi_1^0$?
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Since $\Pi^0_1,\Sigma^0_1\subseteq\Delta^0_2$, and the latter is closed under finite conjunctions, that would be the minimal possibly answer.