Timeline for Large Cardinals Imply a Model of ZFC
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2010 at 14:51 | comment | added | Peter LeFanu Lumsdaine | @Tim: no, the single new set given by the large cardinal itself really is key! We don't use it in the model; we use it as the underlying set of the model. | |
| Nov 8, 2010 at 23:38 | comment | added | Andrés E. Caicedo | @Guillaume: You are correct, but you need to be a bit careful here. Even if there are no inaccessible cardinals, there may be many $\lambda$ such that $V_\lambda$ is a model of set theory. | |
| Nov 8, 2010 at 22:50 | history | edited | Guillaume Brunerie | CC BY-SA 2.5 |
Corrected a mistake that Stefan pointed out
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| Nov 8, 2010 at 21:32 | comment | added | Guillaume Brunerie | In order to build the set of all sets of rank $<\kappa$, you will need transfinite induction on the ordinal $\kappa$ (or something equivalent), so $\kappa$ needs to be a set. You can also see that if $V_\kappa$ is a set, $\kappa$ must also be a set, because it is the set of all ordinals belonging to $V_\kappa$. | |
| Nov 8, 2010 at 20:56 | comment | added | Tim Lewandowski | I think my problem is that the large cardinal axiom gives you a new set, but then we don't really use it in the model. Thinking about it more, it does imply the existence of more than one set, some of them smaller than $\kappa$. | |
| Nov 8, 2010 at 20:52 | vote | accept | Tim Lewandowski | ||
| Nov 8, 2010 at 20:31 | history | answered | Guillaume Brunerie | CC BY-SA 2.5 |