Subalgebras of an Order Sorted Algebra. Lattice of Subalgebras1
نویسنده
چکیده
Let S be an order sorted signature and let U0 be an order sorted algebra of S. A many sorted subset indexed by the sorts of U0 is said to be an OSSubset of U0 if: (Def. 2) It is an order sorted set of S. Let S be an order sorted signature. One can verify that there exists an order sorted algebra of S which is monotone, strict, and non-empty. Let S be an order sorted signature and let U0 be a non-empty order sorted algebra of S. Note that there exists an OSSubset of U0 which is non-empty. One can prove the following proposition 1This work was done during author’s research visit in Bialystok, funded by the CALCULEMUS grant HPRN-CT-2000-00102.
منابع مشابه
Subalgebras of an Order Sorted Algebra. Lattice of Subalgebras
In this paper x denotes a set and R denotes a non empty poset. Next we state two propositions: (1) For all order sorted sets X, Y of R holds X ∩Y is an order sorted set of R. (2) For all order sorted sets X, Y of R holds X ∪Y is an order sorted set of R. Let R be a non empty poset and let M be an order sorted set of R. A many sorted subset indexed by M is said to be an order sorted subset of M ...
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