Algebraic and Arithmetic Lattices . Part I 1 Robert Milewski Warsaw University
نویسنده
چکیده
The scheme LambdaCD deals with a non empty set A, a unary functor F yielding a set, a unary functor G yielding a set, and a unary predicate P, and states that: There exists a function f such that dom f = A and for every element x of A holds if P[x], then f(x) = F(x) and if not P[x], then f(x) = G(x) for all values of the parameters. The following propositions are true: (1) Let L be a non empty reflexive transitive relational structure and x, y be elements of L. If x ¬ y, then compactbelow(x) ⊆ compactbelow(y). (2) For every non empty reflexive relational structure L and for every element x of L holds compactbelow(x) is a subset of CompactSublatt(L). (3) For every relational structure L and for every relational substructure S of L holds every subset of S is a subset of L.
منابع مشابه
Algebraic and Arithmetic Lattices . Part I 1
(1) Let L be a non empty reflexive transitive relational structure and x, y be elements of L. If x ≤ y, then compactbelow(x)⊆ compactbelow(y). (2) For every non empty reflexive relational structure L and for every element x of L holds compactbelow(x) is a subset of CompactSublatt(L). (3) For every relational structure L and for every relational substructure S of L holds every subset of S is a s...
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