Timeline for Decidability of the Axiom of Choice
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 6, 2011 at 19:05 | comment | added | Stefan Geschke | Well, Goedel did come up with the constructible universe $L$ in order to prove the consistency of ZFC assuming the consistency of ZF (and the consistency of GCH). So in this sense $V=L$ is tailored to imply AC. On the other hand, if you are inside a model $V$ of ZF, then $L$ is the smallest inner model of ZF that contains all the ordinals. So in this sense $L$ is a canonical object and it happens to satisfy AC (global choice, even). This shows that $V=L$ is a natural statement, independent of the fact that it implies choice. (I am not saying that ZF+$V=L$ is the right framework for math.) | |
| Feb 24, 2011 at 1:56 | comment | added | user1448 | I don't really have a general method in mind. If the original author were alive, I suppose I could just ask him. In the case of V=L I don't know enough about the context in which it was proposed, so I'd have to suspend judgment. | |
| Feb 24, 2011 at 0:50 | comment | added | Oliver | I don't see how you propose to judge whether an axiom is "tailored to the purpose" or not. Would you say that V=L is "tailored to the purpose"? | |
| Feb 23, 2011 at 19:15 | history | answered | user1448 | CC BY-SA 2.5 |