Timeline for Anti-large cardinal principles
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2017 at 18:31 | comment | added | Zetapology | @NeilBarton Wouldn't it make more sense to look at principles which imply the inconsistency of small large cardinals? This is because these principles actually act like the large cardinals themselves; the weaker the large cardinal axiom is that these principles deny, the closer the principles are to inconsistency with ZFC (viewing ZFC itself as the weakest large cardinal axiom). Just a preference though, not necessary of course. | |
| Apr 26, 2017 at 17:54 | comment | added | Neil Barton | In fact, if we look at the space below the axiom of infinity, the principle ``superexponentiation is not total'' (equivalent to the negation of the Finite Ramsey Theorem over $EFA$) would be a similar principle. In general assertions about fast growing functions behave a bit like large cardinals in the arithmetic realm (Peter Koellner made this point to me, and there's some similar remarks in his SEP article: plato.stanford.edu/entries/large-cardinals-determinacy). | |
| Apr 26, 2017 at 17:50 | comment | added | Neil Barton | @OscarCunningham. Indeed. I regard that as an example of 3 (after all, the axiom of infinity seems like a large cardinal axiom to me). | |
| Apr 26, 2017 at 17:20 | comment | added | Oscar Cunningham | $PA$ is equivalent to $ZF$ with the axiom of infinity replaced by its negation. That fact sort of fits in here. | |
| Apr 26, 2017 at 14:58 | answer | added | Stefan Mesken | timeline score: 5 | |
| Apr 25, 2017 at 0:45 | answer | added | Joel David Hamkins | timeline score: 10 | |
| Apr 24, 2017 at 15:46 | answer | added | Mohammad Golshani | timeline score: 19 | |
| Apr 24, 2017 at 15:10 | answer | added | Joel David Hamkins | timeline score: 14 | |
| Apr 24, 2017 at 14:57 | review | First posts | |||
| Apr 24, 2017 at 15:04 | |||||
| Apr 24, 2017 at 14:56 | history | asked | Neil Barton | CC BY-SA 3.0 |