Re: Which theories hold a true but unprovable statement?

On 20 Feb, 22:20, George Greene wrote:
both PA+~Con(PA) + Con(PA+~Con(PA))
AND PA+~Con(PA) + ~Con(PA+~Con(PA))
are both consistent, IF PA is consistent.

Nope; ~Con(PA+~Con(PA)) is provable in PA+~Con(PA).

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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Relevant Pages

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