Timeline for Is any true sentence in the second-order Peano Axioms provable
Current License: CC BY-SA 2.5
4 events
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| Feb 7, 2010 at 17:28 | comment | added | François G. Dorais | @Mohamed: Con(ZFC) is a first-order statement, so two models of ZFC need not even agree on first-order theory of the natural numbers. | |
| Feb 7, 2010 at 15:48 | comment | added | Mohamed Alaa El Behairy | To clarify: the second order PA is semantically complete, but i am asking about syntactic completeness in the sense that every true statement has a proof using a suitable proof system. As to the set-theoretic issues, does this mean that for every model of ZFC we have a different unique model of the PA? if so is there a canonical model of ZFC which defines the true natural numbers? or is it just a question of what subsets each model allow and they agree on all non-second-order statements | |
| Feb 7, 2010 at 15:18 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
added 664 characters in body
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| Feb 7, 2010 at 15:11 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |