Timeline for Non-principal ultrafilters on ω
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20, 2010 at 22:17 | comment | added | François G. Dorais | @Joel: No, they don't use large cardinals. | |
| Feb 20, 2010 at 6:38 | comment | added | Cory Knapp | Thanks, indeed, François. That gives a more solid answer to my first question. | |
| Feb 20, 2010 at 6:00 | comment | added | Joel David Hamkins | Thanks, François! Do Pincus and Solovay use an inaccessible cardinal in that model (i.e. "the Solovay model")? Or can one do it starting just from ZFC? And do you know models that have ultrafilters on omega, but not on higher cardinals? | |
| Feb 20, 2010 at 5:49 | comment | added | François G. Dorais | A model of DC without ultrafilters on omega was produced by David Pincus and Bob Solovay in Definability of measures and ultrafilters (J. Symb. Logic 42, 1977). I think models without ultrafilters were produced earlier by Andreas Blass, but I don't recall the status of DC in that case. | |
| Feb 20, 2010 at 5:26 | vote | accept | Cory Knapp | ||
| Feb 20, 2010 at 5:26 | comment | added | Cory Knapp | Thanks. The article led me in exactly the direction I was looking. | |
| Feb 20, 2010 at 5:23 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
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| Feb 20, 2010 at 5:12 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |