Timeline for How to define compatible topology for first-order structures?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2022 at 9:15 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
replaced the dead link
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| Aug 30, 2013 at 22:50 | history | edited | Noah Schweber | CC BY-SA 3.0 |
Completely overhauled answer
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| Aug 28, 2013 at 8:11 | comment | added | Thomas Klimpel | I focus on universal Horn structures, because this invalidates the most obvious counterexamples. You stated: "However, note that many intuitively compatible structures are ruled out by your approach", but none of the counterexamples you gave was a universal Horn structure. This is no coincidence, because focusing on universal Horn structures allows us to "essentially" ignore negated relations. (If you define $x<y$ via $(x \leq y) \land \lnot (x=y)$, you see how negation entered the picture for your counterexamples.) | |
| Aug 28, 2013 at 2:06 | comment | added | François G. Dorais | My understanding is limited but I believe the brilliant breakthrough of Priestley's approach resides in combining the upper and lower views into one topology and therefore understanding the inherent duality present in (bounded) lattices. The key to understanding her approach is consumed by understanding the celebrated Priestley duality (which I unfortunately do not yet understand very well). | |
| Aug 28, 2013 at 1:50 | history | answered | Noah Schweber | CC BY-SA 3.0 |