Timeline for Can we have an inverted iterative hierarchy?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 12 at 18:26 | comment | added | Joel David Hamkins | Well, I wish you good luck. My view is that when one finds that one's foundational theory allows for bizarre undesirable phenomenon, it is a reason to adopt a better theory. | |
| May 12 at 18:00 | comment | added | Zuhair Al-Johar | @JoelDavidHamkins, one of the aims from developing such a hierarchy is to remove the obstacles to one-type shift automorphisms. I hope the even/odd problem can be bypassed. | |
| May 12 at 17:58 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
added 557 characters in body; edited tags
|
| May 12 at 16:04 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
deleted 4 characters in body
|
| May 12 at 16:01 | comment | added | Zuhair Al-Johar | @JoelDavidHamkins, $\mathbb Z$ is internal. The $+$ operator on $\mathbb Z$ is defined so that $i+1$ is one type higher than $i$ in stratification. $U$ can be used in Separation. The arguments of $U$ receive equal type indices during stratification, so $U_i$ and $i$ receive the same type. For example we take $\mathbb Z$ to be the set of all acyclic infinitely iterative singletons $\{\{\{\cdots \space \cdots\}\}\}$, fix one of its elements to be $0$ and define $i+1 = \{i\}$. Of course we need to add axioms to support such internal grasp of $\mathbb Z$. | |
| May 12 at 14:40 | comment | added | Joel David Hamkins | Can you let us know whether $U$ is allowed to appear in formulas in the separation scheme? And you use $\mathbb{Z}$ as indices, but is this meant to be the internal version of $\mathbb{Z}$ or the metatheoretic $\mathbb{Z}$? | |
| May 12 at 13:57 | comment | added | Joel David Hamkins | You seem to be interested in models of set theory with automorphisms that change rank. This can happen even in models of ZFC (which extends your theory). Take any computably saturated countable model---it has many automorphisms that change rank on the ordinals. The same is true for any saturated model. (These automorphisms never change the rank by exactly one, however, since ordinals follow the even/odd pattern.) | |
| May 12 at 13:38 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
deleted 493 characters in body
|
| May 12 at 13:37 | history | undeleted | Zuhair Al-Johar | ||
| May 12 at 12:04 | history | deleted | Zuhair Al-Johar | via Vote | |
| May 12 at 12:03 | history | undeleted | Zuhair Al-Johar | ||
| May 12 at 6:24 | history | deleted | Zuhair Al-Johar | via Vote | |
| May 12 at 4:52 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
added 126 characters in body
|
| May 11 at 22:47 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
added 29 characters in body
|
| May 11 at 15:28 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |