Where in the hierarchy $\Sigma_α^β$ does the problem of deciding the truth value of a sentence in ZFC fall?
2026-03-29 12:32:00.1774787520
Where in the $\Sigma_α^β$ hierarchy does the problem of deciding a sentence in ZFC fall?
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A sentence doesn't have a truth value in a theory (such as ZFC). What you can ask about a sentence relative to ZFC is whether that sentence is provable or not provable in ZFC.
The question of whether a sentence is provable in ZFC is $\Sigma^0_1$; in other words, the set of provable sentences is recursively enumerable.