Timeline for Axiom of choice and algebraic tensor product
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2019 at 16:53 | vote | accept | Phil-W | ||
| Mar 10, 2019 at 10:11 | answer | added | Jeremy Rickard | timeline score: 13 | |
| Mar 9, 2019 at 23:44 | comment | added | Gro-Tsen | It is probably worth linking to the analogous question for modules over a (commutative) ring: it turns out, as explained in several answers there, that the map $M^\vee\otimes N^\vee\to(M\otimes N)^\vee$ can fail to be injective (even in the presence of AC, that is). | |
| Mar 9, 2019 at 23:24 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 9, 2019 at 23:11 | comment | added | Phil-W | My question can be broadly intepreted as : what is the status of those statements in ZF ? Are they theorems ? are they equivalent to AC ? are they equivalent to a known weaker axiom ? | |
| Mar 9, 2019 at 23:03 | comment | added | YCor | "Is AC necessary to prove X" technically means "does X implies AC" (probably, in ZF). But this is probably not what you mean. Probably you're asking whether the given statement is a theorem of ZF. | |
| Mar 9, 2019 at 22:54 | history | asked | Phil-W | CC BY-SA 4.0 |