Timeline for Definition of term functions, in universal algebra
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2023 at 7:09 | comment | added | Emil Jeřábek | Good to hear that. | |
| Oct 6, 2023 at 2:59 | comment | added | BAD MAN | I undertand now, I misunderstood the definition. | |
| Oct 5, 2023 at 8:05 | history | edited | YCor |
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| Oct 5, 2023 at 7:02 | comment | added | BAD MAN | And the question came to my mind when I read the Definition 11.1 in Chapter 2. It is about identities and things like $A\models p\approx q$, and there is an obvious ambiguity when the tuple $(x_1,...,x_n)$ is not clear. Also, when I went back to the proof of Theorem 10.3(c) in Chapter 2, I find it hard to show $E^{k}(S)$ is equal to RHS, because of similar problems. | |
| Oct 5, 2023 at 6:53 | comment | added | BAD MAN | I don't know is $X$ allowed to be $\{x\}$, in this case, all terms are of the the form $p(x)$, and obviously the term functions can no longer 'generate' $Sg(X)$, when considering an algebra $A$ and its subset $X$. | |
| Oct 5, 2023 at 6:38 | comment | added | Emil Jeřábek | Why do you think there is a need to "deal" with it? What exactly is the problem? First, when you discuss, say, the set of $n$-ary term functions, you fix a sequence of variables, say $(x_1,\dots,x_n)$ in advance, and consider term in these variables, hence there is no ambiguity. In any case, the sets of terms and term functions are closed under permutations of variables, hence the ambiguity does not matter. | |
| Oct 5, 2023 at 5:08 | history | asked | BAD MAN | CC BY-SA 4.0 |