Timeline for Axiom of Choice and bases of $k$-vector spaces, $k$ fixed
Current License: CC BY-SA 4.0
3 events
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| Jul 28, 2021 at 20:30 | comment | added | Jeremy Rickard | Blass's beautiful and ingenious proof is quite short (the paper is three pages long, and can be found on his web page), so I think the best way for you to answer your question is to read it. But briefly, the answer to the question "why not?" is that, starting with a counterexample to AC (strictly speaking, to the Axiom of Multiple Choice), the vector space without a basis that he constructs is over a field that depends on that counterexample. | |
| Jul 28, 2021 at 19:56 | comment | added | Asaf Karagila♦ | It's an open question. Essentially, Blass' construction, taken "as is", requires you to have fairly complicated fields to encode for the choice function. So it's not clear if you can reduce those to their prime field. | |
| Jul 28, 2021 at 19:51 | history | asked | THC | CC BY-SA 4.0 |