Timeline for Axiom of dependent choice (up to $\omega_1$) and group rank
Current License: CC BY-SA 3.0
13 events
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| Aug 6, 2013 at 9:32 | vote | accept | user38200 | ||
| Aug 6, 2013 at 4:36 | history | edited | Asaf Karagila♦ |
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| Aug 6, 2013 at 4:36 | answer | added | Asaf Karagila♦ | timeline score: 1 | |
| Aug 6, 2013 at 3:14 | comment | added | Asaf Karagila♦ | My guess is that both answers are negative. All sort of Lauchli-like constructions using larger supports should give you a counterexample. The second question seems to be true in $\sf ZF$, there is a bijection between the generators and it extends uniquely. | |
| Aug 6, 2013 at 2:37 | history | edited | user38200 | CC BY-SA 3.0 |
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| Aug 6, 2013 at 2:24 | history | edited | user38200 | CC BY-SA 3.0 |
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| Aug 6, 2013 at 1:47 | comment | added | Asaf Karagila♦ | @Francois: I suppose the meaning is at least one way; otherwise yes. Take $A$ to be free abelian and $B$ free, both with the same set of generators. Should be false, I think. | |
| Aug 6, 2013 at 1:19 | comment | added | François G. Dorais | Isn't the statement of the second paragraph plainly false? | |
| Aug 6, 2013 at 1:13 | comment | added | user38200 | Yes by rank I mean the minimal cardinality of generators. | |
| Aug 6, 2013 at 1:12 | history | edited | user38200 | CC BY-SA 3.0 |
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| Aug 5, 2013 at 15:05 | comment | added | Asaf Karagila♦ | What is "not too big"? By rank do you mean minimal cardinality of generators? | |
| Aug 5, 2013 at 11:07 | review | First posts | |||
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| Aug 5, 2013 at 10:49 | history | asked | user38200 | CC BY-SA 3.0 |