Timeline for Can an acyclic set construction scheme be proved in Ackermann set theory?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2020 at 11:16 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
added 6 characters in body
|
| Mar 19, 2020 at 10:58 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
added 87 characters in body
|
| Feb 21, 2020 at 9:14 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
added 47 characters in body
|
| Feb 21, 2020 at 9:04 | history | edited | Zuhair Al-Johar | CC BY-SA 4.0 |
deleted 2 characters in body
|
| S Sep 16, 2017 at 8:39 | history | bounty ended | CommunityBot | ||
| S Sep 16, 2017 at 8:39 | history | notice removed | CommunityBot | ||
| S Sep 8, 2017 at 7:13 | history | bounty started | Zuhair Al-Johar | ||
| S Sep 8, 2017 at 7:13 | history | notice added | Zuhair Al-Johar | Draw attention | |
| Sep 6, 2017 at 19:45 | comment | added | Zuhair Al-Johar | Yes, you can define "transpassing" using the predicate approach! However, given all the axioms, it won't make any difference whether you define it using predicates or you define it using transitive closure classes since the existence of the later would be proven from Extensionality, Class comprehension, and Transitivity, and all of those are necessarily needed (together with axiom of acyclicity) for acyclic set construction scheme to kick in! That said, it appears to me that it would be nicer to define 'transpassing' in terms of transitive closure classes. | |
| Sep 6, 2017 at 14:56 | comment | added | Peter LeFanu Lumsdaine | It’s not clear to me why a “transitive closure class” exists. Given $z$, we can certainly define a predicate whose extension is the transitive closure of $z$, defined as “every transitive class $C$ with $z \subseteq C$ contains $x$”, but proving that this predicate is represented by a class requires some comprehension axioms. (This isn’t a problem for the rest of your treatment, though — the predicate version is enough for your definition of “transpassing”.) | |
| Sep 6, 2017 at 13:48 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
added 17 characters in body
|
| Sep 5, 2017 at 16:24 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
added 44 characters in body
|
| Sep 5, 2017 at 9:44 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
deleted 3 characters in body
|
| Sep 5, 2017 at 9:36 | history | asked | Zuhair Al-Johar | CC BY-SA 3.0 |