Timeline for Embedding of a poset with "desirable" characteristics
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 5 at 22:12 | comment | added | Pedram | I realized that adding 0 to 𝐷 will make 𝑋 smaller than what I described in my comment earlier. Is that why you added the 0? | |
| Mar 5 at 21:25 | comment | added | Pedram | If D doesn't have a 0, then stage 3 would create a companion element for every element of D since in the absence of 0, no element is an atom, either. Also, in the absence of 0, we can modify the requirement "$x_d$ is strictly above 0" to "$x_d$ is not the minimum element of the final set $X$", right? Or would this violate property 2? | |
| Mar 5 at 20:31 | comment | added | Pedram | I have a couple of clarifying questions (I'm new to some terminologies): 1) In stage 2, is $(D, \succeq)$ the smallest meet-subsemilattice of $(C, \succeq)$ that contains the elements of $\{h(x)|x\in P\}$? 2) Why do you add a 0 to D in stage 2? Is it to guarantee that for every $x, y \in X$, $x\wedge y$ exists in $X$? If so, wouldn't property 2 of my question (the original one, not the strengthening of it) be still satisfied even without adding a 0? Thanks! | |
| Mar 4 at 21:40 | history | edited | Alec Rhea | CC BY-SA 4.0 |
got the succ
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| Mar 4 at 16:23 | vote | accept | Pedram | ||
| Mar 4 at 14:09 | history | edited | Keith Kearnes | CC BY-SA 4.0 |
deleted 13 characters in body
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| Mar 4 at 3:52 | history | answered | Keith Kearnes | CC BY-SA 4.0 |