Timeline for Relations of axioms of choice
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| May 3, 2018 at 21:03 | vote | accept | user44191 | ||
| May 1, 2018 at 11:41 | history | edited | Martin Sleziak |
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| May 1, 2018 at 3:41 | history | edited | user44191 | CC BY-SA 3.0 |
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| May 1, 2018 at 3:30 | comment | added | Joel David Hamkins | But it turns out that actually this foundational issue can be sidestepped with a trick, as I explain in my answer. | |
| May 1, 2018 at 3:29 | answer | added | Joel David Hamkins | timeline score: 12 | |
| May 1, 2018 at 3:13 | comment | added | Joel David Hamkins | Yes, that's right. | |
| May 1, 2018 at 3:13 | history | edited | user44191 | CC BY-SA 3.0 |
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| May 1, 2018 at 3:04 | comment | added | user44191 | @JoelDavidHamkins That prevents me from making a single axiom that unites all of these (at least, in the naive way), but for any definable $X$, I can write the statement $AC_X$, right? | |
| May 1, 2018 at 3:00 | comment | added | Joel David Hamkins | You cannot express the axiom that restricts the statement only to definable $X$, since the property "$X$ is definable" is not definable. | |
| May 1, 2018 at 2:26 | history | edited | user44191 | CC BY-SA 3.0 |
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| May 1, 2018 at 1:59 | history | edited | user44191 | CC BY-SA 3.0 |
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| May 1, 2018 at 1:59 | comment | added | user44191 | @DavidRoberts I do want to do it for more than definable $X$, but it seems to me that that runs into problems with whether you are working "in-model" or over several models, though I'd appreciate any way to correct that! I'll try to clean up the missing nonempties. | |
| May 1, 2018 at 1:55 | comment | added | David Roberts♦ | I would say the converse (That $AC_X$ is true for all sets $X$ implies $AC$) holds. But if you want only definable $X$, that's a bit more subtle. Also, you are probably missing some "nonempty" conditions in your description, but it is clear what you mean. | |
| May 1, 2018 at 1:51 | history | asked | user44191 | CC BY-SA 3.0 |