Timeline for Logic-Compactness in complete lattice
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| 6 hours ago | history | edited | Florian | CC BY-SA 4.0 |
correct a grammar mistake
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| yesterday | comment | added | Florian | @Emil Jeřábek Thanks for your helpful and important suggestions! | |
| yesterday | history | edited | Florian | CC BY-SA 4.0 |
simplified some conditions, and added some conditions
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| yesterday | comment | added | Emil Jeřábek | ... with limit $\sqrt2$, and, say, $x=2$, $y=3$, $z=4$, then $\bigwedge\{x,y\lor z,x_1,x_2,x_3,\dots\}$ does not exist. So in what sense is this “nonexistent element” less than or equal $2=(x\land y)\lor(x\land z)$? | |
| yesterday | comment | added | Emil Jeřábek | ... is not a term over lattices, as there is no $\to$ operation in the language of lattices. So I’m not sure what to make of that. Second, despite having been prompted for it already several times, you still haven’t explained what is supposed to happen WHEN $\bigwedge\Gamma$ DOES NOT EXIST in the lattice in question. This is absolutely crucial. For example, you claim that $\bigwedge\{x,y\lor z,x_1,x_2,x_3,\dots\}\le(x\land y)\lor(x\land z)$ holds in distributive lattices. But $(\mathbb Q,\le)$ is a distributive lattice, and when I take for $x_1,x_2,\dots$ a descending rational sequence ... | |
| yesterday | comment | added | Emil Jeřábek | Hmm, so the question actually asks something completely different from what it looked originally. However, it is still fairly unclear. First, “formulas” are things like $\forall x\,\exists y\,x<y$ that are either true or false; they do not evaluate in any meaningful way to elements of the lattice. It seems that when you write “formulas”, you actually mean “terms over the lattice signature”, which do indeed take values in the lattice. Certainly $y\lor z$ and $(x\land y)\lor(x\land z)$ are terms. (I’m not going to use the square symbols as they are difficult to type.) However, “$x\to y$” ... | |
| yesterday | history | edited | Florian | CC BY-SA 4.0 |
added 4 characters in body
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| yesterday | history | edited | Florian | CC BY-SA 4.0 |
further clarification
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| yesterday | comment | added | Emil Jeřábek | You are making the question more and more unclear. I assume “kind of lattice” just means a class $C$ of lattices, in which case the only way I can read “instance” of “this kind” is that is refers to lattices $L\in C$. But then saying “$\bigwedge\Gamma\le y$ holds for all $L\in C$” makes no sense whatsoever, as $\Gamma$, $\bigwedge\Gamma$, and $y$ only belong to one particular lattice. And you still did not clarify what happens when the meet of $\Gamma$ does not exist. | |
| yesterday | history | edited | Florian | CC BY-SA 4.0 |
to make some expressions more precise
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| yesterday | history | became hot network question | |||
| yesterday | comment | added | Emil Jeřábek | Simultaneously cross-posted at math.stackexchange.com/questions/5115256/… . Please, do not do that. | |
| yesterday | answer | added | Emil Jeřábek | timeline score: 5 | |
| yesterday | comment | added | Emil Jeřábek | If the lattice is not complete, how is the definition of logic compactness involving $\bigsqcap\Gamma$ intended to be interpreted in the first place? | |
| S 2 days ago | review | First questions | |||
| 2 days ago | |||||
| S 2 days ago | history | asked | Florian | CC BY-SA 4.0 |