Timeline for Well-ordering of power set of $\omega$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jul 2, 2016 at 23:01 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
Maybe that will appease the downvoter.
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| Jun 22, 2016 at 16:06 | comment | added | Asaf Karagila♦ | @Andreas: And also because given any "general failure of choice" that we can [symmetrically] force, we can always [symmetrically] force it to happen above rank $\omega+1$, therefore ensuring that the reals are the same as in the ground model, and therefore can be well-ordered. | |
| Jun 22, 2016 at 14:28 | comment | added | Andreas Blass | To formalize (in some sense) Noah's comment, notice that the Jech-Sochor embedding, which puts a big piece of any permutation model into a ZF model, can be done without changing the reals. | |
| Jun 22, 2016 at 12:06 | comment | added | Asaf Karagila♦ | Well, yes, except things like "there is a Dedekind finite set of reals", or other things more or less directly implying that the continuum is not well orderable... :-) | |
| Jun 22, 2016 at 11:56 | comment | added | Noah Schweber | Conversely, any choice principle I can think of can fail without directly impacting the reals - just have failures occur at high rank. | |
| Jun 22, 2016 at 9:32 | comment | added | Asaf Karagila♦ | Also if you're interested in other choice principles, let me know specifically. | |
| Jun 22, 2016 at 9:32 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
added 127 characters in body
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| Jun 22, 2016 at 9:29 | comment | added | Asaf Karagila♦ | I could add a short sketch of a proof later if you're interested. | |
| Jun 22, 2016 at 9:16 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |