Timeline for Why are pure powers of the empty set insufficient as a definition for ordinals?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jun 29 at 3:35 | answer | added | Kristian Berry | timeline score: 1 | |
| Apr 13 at 0:05 | comment | added | Julius Hamilton | Ok. Yeah I got confused about how to describe the Zermelo ordinals I guess. But yeah, seems like it’s a common question: math.stackexchange.com/questions/2975907/… | |
| Apr 10 at 15:03 | history | edited | Julius Hamilton | CC BY-SA 4.0 |
added 2 characters in body
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| Apr 10 at 3:25 | answer | added | Invariance | timeline score: 1 | |
| Apr 10 at 2:36 | history | became hot network question | |||
| Apr 9 at 22:31 | comment | added | Michael Carey | Every well-ordered set is isomorphic to a unique ordinal, that is why we say ordinals "measure" the length of well-orderings. | |
| Apr 9 at 22:23 | comment | added | Double Knot | Re your "The following sequence is called the “pure” or “irreducible” power sets of the empty set", the sequence is neither pure not irreducible power sets of empty sets, unlike ZF set theory, in Zermelo set theory these are just canonical representation perhaps realized as a well-ordered set constructed using the empty set, any ordinal itself is defined in terms of an order type (not a set) of all well-ordered sets in its equivalence class following Hume's principle... | |
| Apr 9 at 19:32 | comment | added | J D | "We want to deduce logical preconditions on property y, without knowing anything about property y. Simultaneously, we want to deduce property y as following from key logical preconditions X, while at the same time having no point of reference for what premises X should look like, except for with recourse to the as-of-yet undetermined y." I didn't read your post too closely, but it seems related to impredicativity. en.wikipedia.org/wiki/Impredicativity | |
| Apr 9 at 19:28 | history | edited | J D |
edited tags; edited tags
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| Apr 9 at 19:21 | comment | added | Conifold | These are called Zermelo ordinals:"With this definition each natural number is a singleton set. So, the property of the natural numbers to represent cardinalities is not directly accessible; only the ordinal property (being the nth element of a sequence) is immediate. Unlike von Neumann's construction, the Zermelo ordinals do not extend to infinite ordinals." That's why they are insufficient. | |
| Apr 9 at 19:11 | answer | added | ac15 | timeline score: 6 | |
| Apr 9 at 18:58 | review | Close votes | |||
| Apr 18 at 3:11 | |||||
| Apr 9 at 18:36 | history | asked | Julius Hamilton | CC BY-SA 4.0 |