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I'd say Con(ZF) isn't known to be undecidable--it's only undecidable if it's true. If it's false, that fact is $\Sigma^0_1$ and therefore provable. We want a sentence that's $\Sigma^0_2$ or higher.
This might be an examplealmost-example: http://www.cs.uchicago.edu/~simon/RES/collatz.pdf
It proves that a generalization of the 3n+1 conjecture is $\Pi_2$-complete. But it's not quite what is asked, since it's about a family of problems rather than a single sentence.
I'd say Con(ZF) isn't known to be undecidable--it's only undecidable if it's true. If it's false, that fact is $\Sigma^0_1$ and therefore provable. We want a sentence that's $\Sigma^0_2$ or higher.
This might be an example: http://www.cs.uchicago.edu/~simon/RES/collatz.pdf
It proves that a generalization of the 3n+1 conjecture is $\Pi_2$-complete. But it's not quite what is asked, since it's about a family of problems rather than a single sentence.
I'd say Con(ZF) isn't known to be undecidable--it's only undecidable if it's true. If it's false, that fact is $\Sigma^0_1$ and therefore provable. We want a sentence that's $\Sigma^0_2$ or higher.
This might be an almost-example: http://www.cs.uchicago.edu/~simon/RES/collatz.pdf
It proves that a generalization of the 3n+1 conjecture is $\Pi_2$-complete. But it's not quite what is asked, since it's about a family of problems rather than a single sentence.
I'd say Con(ZF) isn't known to be undecidable--it's only undecidable if it's true. If it's false, that fact is $\Sigma^0_1$ and therefore provable. We want a sentence that's $\Sigma^0_2$ or higher.
This might be an example: http://www.cs.uchicago.edu/~simon/RES/collatz.pdf
It proves that a generalization of the 3n+1 conjecture is $\Pi_2$-complete. But it's not quite what is asked, since it's about a family of problems rather than a single sentence.
