Timeline for Continuum function maximum
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2022 at 2:18 | vote | accept | Ember Edison | ||
| Dec 26, 2021 at 10:53 | comment | added | Ember Edison | So, Do you think we are missing the "puzzle pieces" that make the concept of "continuum function maximum" to absolute, or is there no such concept at all? I feel like I've been reading papers on PCF theory for the past few days and it doesn't really help with this goal... | |
| Dec 26, 2021 at 10:49 | comment | added | Ember Edison | This doesn't sound like a restriction on continuum function other than the "strongly inaccessible" prohibition. I was also recently discussing with my friend whether "Is there a model about $2^{\kappa}$ is $\kappa$-weakly-inaccessible for every infinite cardinal $\kappa$". | |
| Dec 26, 2021 at 6:46 | comment | added | Noah Schweber | That said, here's one interesting result: it is consistent modulo large cardinals that $2^\kappa$ is weakly inaccessible for every infinite cardinal $\kappa$. See here. If you'd like, I can incorporate these comments into my answer proper. | |
| Dec 26, 2021 at 6:44 | comment | added | Noah Schweber | @EmberEdison I think once we start asking global questions we'll quickly wind up with open problems. For example, even "$2^\kappa>\kappa^+$ for every infinite cardinal $\kappa$" involves large cardinals. I think some care will need to go into formulating such a question in such a way that it is neither trivial nor ultra-wide-open. | |
| Dec 26, 2021 at 6:26 | comment | added | Ember Edison | So Can we well-define "the maximization of the growth rate of the continuum function"? | |
| Dec 26, 2021 at 5:21 | history | answered | Noah Schweber | CC BY-SA 4.0 |