Timeline for Aleph 0 as a large cardinal
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 13 at 4:44 | comment | added | Lucenaposition | Note that $\omega$ also satisfies the infinitary Ramsey theorem. | |
| Aug 25, 2023 at 19:43 | comment | added | Keith Millar | I know this is a very old answer, but I'd like to point out that ω is measurable in the sense that V admits Lω,ω-elementary embeddings into models which preserve ordinals below ω and not ω itself; the Lκ,κ-elementarity of the embedding when κ is uncountable is why the model V embeds into is an inner model. | |
| Jun 4, 2018 at 8:07 | comment | added | Morteza Azad | (+1) Interesting summary, Amit! I enjoyed reading your answer! :-) | |
| Nov 25, 2010 at 8:56 | vote | accept | arsmath | ||
| Nov 10, 2010 at 8:13 | comment | added | arsmath | Thanks. I half-expected that there was a succinct characterization in terms of some general property somewhere in the literature. "Everything that happens for $\aleph_0$ happens again" has the flavor of a reflection principle, and there's a big literature on reflection principles, so I found it plausible that it had a tidy answer. | |
| Nov 10, 2010 at 7:37 | history | answered | Amit Kumar Gupta | CC BY-SA 2.5 |