Timeline for Total order on the powerset
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 24, 2011 at 13:52 | vote | accept | mathahada | ||
| Jan 22, 2011 at 18:31 | comment | added | Joel David Hamkins | See also this related MO question: mathoverflow.net/questions/37272/are-all-sets-totally-ordered | |
| Jan 22, 2011 at 17:57 | comment | added | Andreas Blass | The first model of set theory that satisfies the ordering principle ("every set can be totally ordered") but not the axiom of choice was a permutation model (of set theory with atoms) constructed by Mostowski in the late 1930's. For models of ZF (thus without atoms), Cohen's original model will work. That follows from the theorem of Halpern and Levy (in the late 1960's) that this model satisfies the Boolean prime ideal theorem, which implies the ordering principle. | |
| Jan 22, 2011 at 15:48 | history | edited | Chris Eagle | CC BY-SA 2.5 |
added 142 characters in body
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| Jan 22, 2011 at 15:28 | history | answered | Chris Eagle | CC BY-SA 2.5 |