Timeline for Preimage of a sublocale by a morphism of locales: description by nucleus?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 3 at 14:12 | comment | added | Simon Henry | @Gro-Tsen I've added an "unbounded" description - this is the best I think is doable in term of "logical simplicity" but maybe there are some simplification (for e.g. by wirrting more explicitely what happen when we iterate $j_0$). | |
| Dec 3 at 14:10 | history | edited | Simon Henry | CC BY-SA 4.0 |
added 1059 characters in body
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| Dec 3 at 13:39 | comment | added | Simon Henry | If you are happy with formula that include an ** unbounded ** join or meet, that is indexed by either proper class or at least sets whose size depends on the size of the frames (for e.g. running over all ordinals, or all elements of one of the two frames) then I think I can write down a formula. Back when I was thinking at related problems, I was in a setting where the frame where large sets (due to the lack of power sets) and I needed to find expression that only involved "small" operations - and this turned out to be impossible. | |
| Dec 3 at 13:08 | comment | added | Gro-Tsen | I should note that I'm not necessarily looking for a formula that is a finite expression in the alphabet $\land,\lor,\Rrightarrow,j,f^*,f_*$. For example, the formulas given in this answer to another question of mine involve a $\bigwedge$ (infinite meet) in the frame, which is fine by me. Do you think that even with such infinite operations it is still impossible to express the preimage nucleus? | |
| Dec 2 at 20:28 | history | answered | Simon Henry | CC BY-SA 4.0 |