Inverse Limits of Many Sorted Algebras
نویسنده
چکیده
We adopt the following rules: P denotes a non empty poset, i, j, k denote elements of P , and S denotes a non void non empty many sorted signature. Let I be a non empty set, let us consider S, let A1 be an algebra family of I over S, let i be an element of I, and let o be an operation symbol of S. One can verify that (OPER(A1))(i)(o) is function-like and relation-like. Let I be a non empty set, let us consider S, let A1 be an algebra family of I over S, and let s be a sort symbol of S. Note that (SORTS(A1))(s) is functional. Let us consider P , S. An algebra family of the carrier of P over S is called a family of algebras over S ordered by P if it satisfies the condition (Def. 1). (Def. 1) There exists a many sorted function F of the internal relation of P such that for all i, j, k if i ≥ j and j ≥ k, then there exists a many sorted function f1 from it(i) into it(j) and there exists a many sorted function f2 from it(j) into it(k) such that f1 = F (j, i) and f2 = F (k, j) and F (k, i) = f2 ◦ f1 and f1 is a homomorphism of it(i) into it(j).
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