Timeline for What notions are used but not clearly defined in modern mathematics?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2021 at 2:38 | comment | added | Timothy Chow | @AndrésE.Caicedo What I have most commonly seen is the claim that there is no precise definition of a large cardinal axiom. | |
| Nov 19, 2015 at 18:57 | comment | added | Burak | @AndrésCaicedo Sorry for deleting the comment. I realized after posting the comment that one side of what I had mind is problematic. But I should add the question back so that your comment makes more sense. (I was simply asking the historical reason of the use of the phrase "definable sets of reals" for prejective sets and whether it had anything to do with $\mathcal{L}_{\omega_1 \omega}$ definability in the field of real numbers.) | |
| Nov 19, 2015 at 18:53 | comment | added | Andrés E. Caicedo | @Burak These are precisely the sets that are (first-order) definable from parameters in $(\mathbb R,\mathbb N,+,\times)$. | |
| May 27, 2015 at 9:44 | comment | added | Duchamp Gérard H. E. | Maybe the definition of a what is a set itself ? (I am not a specialist of ZFC) | |
| Feb 26, 2011 at 21:20 | comment | added | Andrés E. Caicedo | Yes, this is in accordance with what I meant: It makes sense to think of this as a "large cardinal notion" (just as with most rungs of the ladder that is the consistency strength hierarchy) but I wouldn't call it a "large cardinal". | |
| Feb 26, 2011 at 21:11 | comment | added | Joel David Hamkins | Andres, regarding your proposal that weakly inaccessible cardinals cover all large cardinal notions, how about the notion by which $\theta$ is fairly big if $V_\theta\satisfies$ ZFC? The least such cardinal is not weakly inaccessible, since it has cofinality $\omega$, but I would still regard this as a large cardinal notion. | |
| Feb 26, 2011 at 20:44 | history | answered | Andrés E. Caicedo | CC BY-SA 2.5 |