Timeline for The disjunction property in Peano Arithmetic?
Current License: CC BY-SA 3.0
10 events
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| Apr 28, 2011 at 1:57 | comment | added | Alex Gavrilov | Joel, there is a gap. Applying the lemma, we may get $\phi$ provably equivalent to $\psi$. In this case $\phi\vee\psi$ is equivalent to $Con(PA)$. Then, the lenghts of nonstandard proofs are nonstandard numbers, which may be incompatible. So, we need another argument to show that $\phi\vee\psi$ can be proved. | |
| Apr 27, 2011 at 15:30 | comment | added | none | OK, I don't know Smullyan's double recursion theorem, but Joel's answer is certainly more likely than mine to be right. | |
| Apr 27, 2011 at 14:54 | comment | added | none | Hmm, well, if you've got another answer please feel free to post it; I think this should be an easy problem but I keep getting stuck with my proof. Or I might try again later in the day. | |
| Apr 27, 2011 at 14:30 | comment | added | Carl Mummert | Yes, I did miss that. I have deleted my answer, which didn't consider the syntactic classes of the formulas. | |
| Apr 27, 2011 at 14:00 | history | edited | none | CC BY-SA 3.0 |
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| Apr 27, 2011 at 13:55 | history | edited | none | CC BY-SA 3.0 |
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| Apr 27, 2011 at 13:49 | history | edited | none | CC BY-SA 3.0 |
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| Apr 27, 2011 at 13:43 | history | edited | none | CC BY-SA 3.0 |
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| Apr 27, 2011 at 13:24 | history | edited | none | CC BY-SA 3.0 |
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| Apr 27, 2011 at 13:18 | history | answered | none | CC BY-SA 3.0 |