Timeline for Why is choice needed in Ellis' Lemma?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2022 at 14:06 | comment | added | Peter LeFanu Lumsdaine | So should Todorcevic have written “Pick by Zorn’s lemma a minimal non-empty compact subsemigroup”, or is he working with the convention that all semigroups are non-empty? | |
| Feb 28, 2022 at 13:37 | history | became hot network question | |||
| Feb 28, 2022 at 9:44 | comment | added | Clement Yung | @YairHayut according to a comment of this answer, the Ultrafilter Lemma is sufficient for Ellis' Lemma. | |
| Feb 28, 2022 at 9:08 | comment | added | Yair Hayut | Is it known whether the axiom of choice is necessary for this result? | |
| Feb 28, 2022 at 8:06 | history | edited | Jochen Wengenroth | CC BY-SA 4.0 |
Correction $P\neq\emptyset$.
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| Feb 28, 2022 at 7:22 | vote | accept | Clement Yung | ||
| Feb 28, 2022 at 7:12 | answer | added | Nick S | timeline score: 9 | |
| Feb 28, 2022 at 6:35 | comment | added | François G. Dorais | A simple counterexample would be the discrete semigroup $\{a,b,ab\}$ where $a,b$ are commuting idempotents. Then $\{a\}$ and $\{b\}$ are the minimal subsemigroups but the intersection of the two is empty. | |
| Feb 28, 2022 at 6:10 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added a Google Books link
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| Feb 28, 2022 at 6:01 | comment | added | Clement Yung | @NickS you're right, thanks! Can you make that an answer? | |
| Feb 28, 2022 at 5:42 | comment | added | Nick S | What if $R=\emptyset$? Note that in Zorn Lemma approach, the nested intersection of non-empty compact sets is non-empty, but without the nestedness you may get the empty set. | |
| Feb 28, 2022 at 5:26 | history | asked | Clement Yung | CC BY-SA 4.0 |