Subalgebras of an Order Sorted Algebra. Lattice of Subalgebras
نویسنده
چکیده
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 if: (Def. 1) It is an order sorted set of R. Let R be a non empty poset and let M be a non-empty order sorted set of R. Note that there exists an order sorted subset of M which is non-empty.
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