Timeline for Does ZFC prove the universe is linearly orderable?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2012 at 12:46 | comment | added | Joel David Hamkins | See related question on whether there can be a global linear order without a global well-order: mathoverflow.net/questions/111370/… | |
| Nov 3, 2012 at 7:19 | vote | accept | Asaf Karagila♦ | ||
| Nov 2, 2012 at 21:58 | comment | added | Asaf Karagila♦ | Oh. I see. You're pointing out that ZFC cannot prove that there is an ordinal definable linear ordering. How does that help to answer the question, though? After all, ZFC does not prove V=OD. | |
| Nov 2, 2012 at 21:17 | comment | added | Ashutosh | By Solovay's model I meant the model obtained by Levy collapsing an inaccessible - AC holds here; the choice free model is obtained by passing to HOD(R). | |
| Nov 2, 2012 at 20:59 | comment | added | Asaf Karagila♦ | I should also point out that there are simpler ways to prove there is no definable linear ordering of the universe without the axiom of choice. Simply add a non-linearly ordered set (e.g. amorphous sets). | |
| Nov 2, 2012 at 20:46 | comment | added | Asaf Karagila♦ | Ashutosh, while you are correct, you should also note that I asked about ZFC, not about ZF. | |
| Nov 2, 2012 at 19:46 | comment | added | Ashutosh | In Solovay's model, there is no ordinal definable non measurable set of reals. Hence there cannot be an ordinal definable linear ordering of power set of reals because one can pass, in a definable way, from such an ordering to a non measurable set as follows: Work in Cantor space. Write x~y iff they agree on all but finitely many bits. Restrict your ordering to the ~ equivalence classes. Let X be the set of those reals x such that the eq class containing x precedes the one containing x' where x' is obtained by changing all bits of x. Then X is not Lebesgue measurable. | |
| Oct 28, 2012 at 17:19 | vote | accept | Asaf Karagila♦ | ||
| Nov 2, 2012 at 13:53 | |||||
| Oct 27, 2012 at 18:32 | answer | added | Ali Enayat | timeline score: 8 | |
| Oct 27, 2012 at 11:47 | answer | added | Joel David Hamkins | timeline score: 15 | |
| Oct 27, 2012 at 1:20 | history | asked | Asaf Karagila♦ | CC BY-SA 3.0 |