Timeline for Can we prove set theory is consistent?
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2010 at 11:22 | vote | accept | Andrea Ferretti | ||
| Apr 27, 2010 at 11:35 | comment | added | Carl Mummert | We can prove the consistency of PA in Set1 by pointing out that the natural numbers are a model. From the POV of a set theorist, this is quite similar to proving the consistency of ZFC in Set1 by pointing out that V<sub>κ</sub>, κ inaccessible, is a model. There are differences between PA and ZFC but the overall method is parallel. The reason these proofs work is that the semantics of informal theories like Set1 are very strong. In formalized PA, I have to worry about nonstandard models. In Set1, I don't: I can just grab the actual natural numbers and work with them. | |
| Apr 27, 2010 at 0:11 | history | answered | Carl Mummert | CC BY-SA 2.5 |