Timeline for Result that follows from ZFC and not ZF but are strictly weaker than choice
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2012 at 21:12 | comment | added | arsmath | No worries, Asaf. | |
| Nov 25, 2012 at 19:39 | comment | added | Asaf Karagila♦ | arsmath, I was just complementing. Didn't argue that you gave a "duplicated" answer. | |
| Nov 25, 2012 at 19:30 | comment | added | arsmath | Right, but it's not equivalent to it, which if I understand the intent of the original question properly, makes it a distinct example. | |
| Nov 25, 2012 at 18:18 | comment | added | Goldstern |
In fact, the Hahn-Banach theorem is (in one version) equivalent to the existence of finitely additive probability measure on every Boolean algebra (whereas an ultrafilter or prime ideal can be seen as a finitely additive $\{0,1\}$-valued measure).
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| Nov 25, 2012 at 13:54 | comment | added | Asaf Karagila♦ | The Hahn-Banach theorem is a consequence of the Boolean Prime Ideal Theorem mentioned by Stefan Geschke below, by the way. | |
| Nov 25, 2012 at 13:15 | history | answered | arsmath | CC BY-SA 3.0 |