Timeline for How do we formally construct the successor universe $\mathscr{U}^+$ of a universe $\mathscr{U}$ in $\mathsf{ZFC}$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2018 at 0:49 | history | edited | Sridhar Ramesh | CC BY-SA 4.0 |
Not every universe with U as an element has the successor to U as an element; namely, the successor to U does not have itself as an element.
|
| Nov 18, 2018 at 23:57 | comment | added | Noah Schweber | @Jxt921 That implication isn't provable in ZFC either - what is provable is that every universe has at most one successor, and that "every universe has a successor" is equivalent to "there is no largest inaccessible." | |
| Nov 18, 2018 at 21:55 | comment | added | Jxt921 | You are right. I apologize for my poor wording. I edited the title and the question. First of all, I wanted to write "construct" instead of "define". Second, I wanted to prove not the existence of a universe in $\mathsf{ZFC}$, but the implication "$\mathscr{U}$ exists $\Longrightarrow \mathscr{U}^+$ exists". | |
| Nov 18, 2018 at 21:03 | history | edited | Andrej Bauer | CC BY-SA 4.0 |
added 182 characters in body
|
| Nov 18, 2018 at 20:56 | history | answered | Andrej Bauer | CC BY-SA 4.0 |