Timeline for Which models of set theory are locally presentable?
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7 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2016 at 22:30 | comment | added | Theo Johnson-Freyd | Ah, sorry for the notation! By "is the identity on finite sets" I mean something less strict than it sounds --- perhaps I should have said "is the identity on finite cardinalities". | |
| Feb 16, 2016 at 2:25 | comment | added | Joel David Hamkins | If what you want is an $\in$-embedding from $V$ to $L$, this is related to my question mathoverflow.net/q/101821/1946, which is still open, but in joint work with Woodin, Magidor and others, we have a bunch of partial results. | |
| Feb 16, 2016 at 2:21 | comment | added | Joel David Hamkins | Gödel's constructible universe is usually denoted by L, and the full set-theoretic universe is usually denoted by V. If these are different, then you can't map V to L with a functor that is the identity on finite sets, since not all finite sets will be in L. If x is not in L, then {x} is a finite set that is not in L. | |
| Feb 16, 2016 at 2:18 | comment | added | Theo Johnson-Freyd | @JoelDavidHamkins No, because it's not a perfectly well-posed question, because I don't really know what a "model of sets" is. But here's a related question. If I'm not mistaken, among the universe U of sets, there some but not all of the sets are "constructible", which I think is called V. Is there a functor from U to V that is the identity on finite sets and takes colimits to colimits? It should be a sort of "rounding up" functor. | |
| Feb 15, 2016 at 20:21 | comment | added | Joel David Hamkins | Is there a purely set-theoretic manner of asking the question? | |
| Feb 15, 2016 at 18:53 | answer | added | Simon Henry | timeline score: 6 | |
| Feb 15, 2016 at 18:29 | history | asked | Theo Johnson-Freyd | CC BY-SA 3.0 |