Timeline for Finite versions of Godel' s incompleteness
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2012 at 14:15 | vote | accept | Mirco A. Mannucci | ||
| Jun 29, 2012 at 10:51 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
typo
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| Jun 29, 2012 at 10:10 | comment | added | Joel David Hamkins | Thanks abo, I have edited to 0=1. The answer provides a negative solution to the second question, since it provides a theory that is $k$-inconsistent, but does not $k$-prove its own $k$-consistency, contrary to the equivalence stated in the question. It is true, however, that this is violating what might be regarded as the "easy" direction of the theorem, and it might be more interesting to violate the other implication. | |
| Jun 29, 2012 at 10:07 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Jun 29, 2012 at 5:30 | comment | added | abo | Also, it's early in the morning, but in order to provide a negative answer to the second question, don't you need to provide a theory which k-proves its own k-consistency (and which is k-consistent)? | |
| Jun 29, 2012 at 5:16 | comment | added | abo | I think it should be PA + 0 = 1 (rather than the unequal sign between 0 and 1). | |
| Jun 29, 2012 at 0:33 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Jun 29, 2012 at 0:21 | comment | added | Joel David Hamkins | Oh yes, I also am waiting for the others to chime in with an answer to your second question. And meanwhile, I shall look forward to your infinitary question! Catch you tomorrow... | |
| Jun 29, 2012 at 0:16 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Jun 29, 2012 at 0:14 | comment | added | Mirco A. Mannucci | Fast as usual Joel! Nice answer: for the time being I have given you my vote, let us see what others come up with. Meanwhile, I anticipate to you that my next question will be on the other side of the spectrum: a bit of heavy duty ultra-INfinitism never hurts! | |
| Jun 28, 2012 at 23:59 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Jun 28, 2012 at 23:50 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |