Timeline for Is Extensionality needed for the incompleteness of very weak set theories?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29, 2015 at 14:05 | comment | added | Joel David Hamkins | Well, you could have a theory that says ST holds on a part of the universe, and then there is another part which may be totally crazy, with extensionality failing utterly there. This would still support coding, because of the sane part. | |
| Oct 29, 2015 at 13:57 | vote | accept | Frode Alfson Bjørdal | ||
| Oct 29, 2015 at 13:55 | comment | added | Frode Alfson Bjørdal | Thanks for this! I am interested in some theory where extensionality fails utterly. May one achieve this by bisimulation, I wonder. In other words: if $ST^-$ is $ST$ minus extensionality, may it be that $ST^-$ interprets $ST$ or enough of $ST$ to arithmetize? \vspace{2pt} On the other hand. The sets created by adjunction over one empty set only invoke identity, and I do not have problems with identity. So it seems that I can accept the controlled manner you invoke for doing the coding ... | |
| Oct 29, 2015 at 13:45 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |