Gödel Without (Too Many) Tears

Re:Gödel Without (Too Many) Tears by cousin_it on Monday September 30, 2013 @03:46PM (#6471855)

If Peano arithmetic (PA) is consistent, the following statements are true but not provable in PA:

1) Consistency of PA

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Re:Gödel Without (Too Many) Tears by cwzwarich on Monday September 30, 2013 @06:45PM (#6472868)

But that's not much of a practical problem, since ZF set theory proves them both.

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Re:Gödel Without (Too Many) Tears by wfn on Monday September 30, 2013 @07:12PM (#6472969)

Ah, but the consistency of ZFC itself is undecidable from within ZFC! [1] I see what you're saying; it's quite the rabbit hole, however.

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