Timeline for Compactness and omega models
Current License: CC BY-SA 3.0
3 events
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| Jul 22, 2016 at 13:11 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Jul 22, 2016 at 12:53 | comment | added | Zuhair Al-Johar | But T+S in your example is not provable by compactness. Anyhow. OK then take the question to be about what property of T+S. I once thought for example that if T is consistent with for all naturals (phi) then if each instance of S states: the standard natural n fulfills phi, then T+S would have an omega model if T had an omega model. It appears that what gives rise to the nonstandards is having an opposition between a theorem of T and what scheme S is asserting. If we have no such opposition then it appears that T+S would have an omega model if T had one. | |
| Jul 22, 2016 at 11:58 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |