Timeline for How closely do ordinal collapsing functions relate to Skolem hulls?
Current License: CC BY-SA 4.0
6 events
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| Sep 12, 2023 at 2:30 | history | edited | C7X | CC BY-SA 4.0 |
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| Jul 14, 2023 at 22:03 | comment | added | C7X | I must have been seeing the essence of Skolemizing as the elementarity conditions it implies. But then all we need is an internal axiomatization of $C$ coming from the clauses of the definition, and then once we have that, $C(\alpha)$ is a Skolem hull taken in $(\mathsf{Ord},+,\varphi)$ which is elementary for Holo's formulae. (I may have been associating L-S too closely with generating models of set theory when it's perfectly good for e.g. generating groups.) | |
| Jul 14, 2023 at 16:45 | comment | added | Joel David Hamkins | Since the essence of Skolemizing is to close a set under a function defined on a larger domain, it doesn't seem unreasonable to describe any instance of that phenomenon as a Skolem hull. | |
| Jul 14, 2023 at 12:25 | comment | added | Holo | Although it appears that the operators above don't include $<$ in them, so it is not truely the same as the Skolem hull of the above Skolem functions | |
| Jul 14, 2023 at 12:18 | comment | added | Holo | The ordinals are well ordered, so the definable elements are closed under the Skolem functions defined as "take the minimal witness of ∃yφ(x,y)", so the closure operator on sets of ordinals can in fact looked at as a Skolem hull operator | |
| Jul 14, 2023 at 6:07 | history | asked | C7X | CC BY-SA 4.0 |