Timeline for Is there an "anti-choice axiom"?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2022 at 12:02 | history | edited | rimu | CC BY-SA 4.0 |
deleted 3 characters in body
|
| Feb 12, 2022 at 21:46 | comment | added | Asaf Karagila♦ | Since your edit completely invalidated my efforts to answer your question, I think I'll give someone else the chance to address your new question. Good luck! | |
| Feb 12, 2022 at 20:50 | history | became hot network question | |||
| Feb 12, 2022 at 16:38 | history | edited | rimu | CC BY-SA 4.0 |
added 290 characters in body
|
| Feb 12, 2022 at 15:00 | answer | added | Asaf Karagila♦ | timeline score: 20 | |
| Feb 12, 2022 at 14:41 | comment | added | rimu | @Gro-Tsen I actually thought in terms of well-ordering but decided to write in terms of choice... But in terms of a choice function, my "choice set" would be a set X for which every family $(X_i)_{i\in I}$ of subsets has a choice function. | |
| Feb 12, 2022 at 14:09 | comment | added | Gro-Tsen | There are two “parameters” in a putative choice situation (when asking if $\prod_{i\in I} X_i$ is inhabited provided the $X_i$ are): the set $I$ of indices, and the set $X = \bigcup_{i\in I} X_i$ in which the values are taken. I think you're talking about $I$ here, but it might be worth clarifying, and maybe thinking about $X$ as well. | |
| Feb 12, 2022 at 13:33 | comment | added | Dave L Renfro | Of possible related interest: What's between the finite and the infinite? and Axiom of choice for sets of finite sets and this paper: John Horton Conway, Effective implications between "finite" choice axioms, pp. 439-458 in Mathias/Rogers (editors), Cambridge Summer School in Mathematical Logic, Lecture Notes in Mathematics #337, Springer-Verlag, 1973 (MR 50 #12725; Zbl 279.02047). | |
| Feb 12, 2022 at 13:22 | comment | added | rimu | @MattF. The reason I am not that happy about the axiom of determinacy is that it is a statement about the set of all countable integer sequences and does not provide insight about all non-choice sets -- at least in the form in which it is stated. But maybe there is another formulation. | |
| Feb 12, 2022 at 13:08 | comment | added | user44143 | The standard example is AD + DC, where AD refutes choice for the continuum, and DC gives choice for countable sets. en.wikipedia.org/wiki/… | |
| Feb 12, 2022 at 12:47 | history | asked | rimu | CC BY-SA 4.0 |