Timeline for Is the partial order of all equations in the signature of magmas a lattice?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22 at 20:38 | vote | accept | user107952 | ||
| S Nov 19 at 17:12 | history | bounty ended | user107952 | ||
| S Nov 19 at 17:12 | history | notice removed | user107952 | ||
| Nov 19 at 6:08 | answer | added | Keith Kearnes | timeline score: 9 | |
| Nov 13 at 1:17 | comment | added | C7X | If this question has a negative answer, it may be possible to resolve it by looking through the implication graph produced by Terence Tao's recent equational theories project, searching for pairs of nodes without least upper bounds or greatest lower bounds. The table of implications is available through this page. | |
| Nov 12 at 23:30 | comment | added | Peter Taylor | In general, $p(\vec{x})=q(\vec{x})$ implies $r(p(\vec{x}), q(\vec{x}), \vec{y}) = r(q(\vec{x}), p(\vec{x}), \vec{y})$. By using $r_i$ of arity four or more we can generate arbitrarily many lower bounds on a pair of equations, and in general there's no reason to suppose that these lower bounds are mutually comparable. | |
| Nov 12 at 11:47 | comment | added | Peter Taylor | You have least and greatest elements $x=x$ and $x=y$, so the question is whether two elements can have multiple incomparable common maximal lower / minimal upper bounds. | |
| S Nov 11 at 18:25 | history | bounty started | user107952 | ||
| S Nov 11 at 18:25 | history | notice added | user107952 | Draw attention | |
| Oct 27 at 19:07 | comment | added | user107952 | @bof I don't know, but if it has neither, that would answer my question. | |
| Oct 27 at 0:46 | comment | added | bof | Do the associative law and the commutative law have a least upper bound and/or a greatest lower bound in your partial order? | |
| Oct 26 at 17:21 | history | edited | LSpice | CC BY-SA 4.0 |
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| Oct 26 at 16:44 | history | asked | user107952 | CC BY-SA 4.0 |