Timeline for A question about large cardinal axioms.
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 13, 2011 at 18:18 | comment | added | Garabed Gulbenkian | Does there or can there exist a large cardinal axiom A such that (1) A is local (2) "Supercompact"<A (3) A is stronger than "Supercompact" in consistency strength? | |
| May 3, 2011 at 14:58 | vote | accept | Garabed Gulbenkian | ||
| May 3, 2011 at 17:09 | |||||
| May 3, 2011 at 2:17 | comment | added | Andreas Blass | @Joel: I didn't intend to imply that this is a nonlinearity in either of the orders (size or consistency strength). It's just a disagreement between the two orders. | |
| May 3, 2011 at 0:35 | comment | added | Joel David Hamkins | Similarly, Supercompact $\lt$ $\Sigma_3$-reflecting on the proposed order, even though $\Sigma_3$-reflecting cardinals are very weak in consistency strength (below Mahlo, or even just ZFC, if you drop inaccessibility requirement). | |
| May 3, 2011 at 0:33 | comment | added | Joel David Hamkins | But Andreas, does this actually show non-linearity in the proposed order? I don't think so. After all, from the existence of both a supercompact and a huge, we can prove that the least huge is smaller than the least supercompact, and so Huge $\lt$ supercompact in this order. The point instead is that $\lt$ is not the right order, since it differs so strongly from the consistency strength order. A more extreme example would be that Huge $\lt$ $\Sigma_2$-reflecting, since $\Sigma_2$ reflecting cardinals will reflect hugeness, but this is a strong reversal of the consistency strength order. | |
| May 3, 2011 at 0:23 | history | answered | Andreas Blass | CC BY-SA 3.0 |