Auxiliary and Approximating Relations1
نویسنده
چکیده
The aim of this paper is to formalize the second part of Chapter I Section 1 (1.9–1.19) in [10]. Definitions of Scott’s auxiliary and approximating relations are introduced in this work. We showed that in a meet-continuous lattice, the way-below relation is the intersection of all approximating auxiliary relations (proposition (40) — compare 1.13 in [10, pp. 43–47]). By (41) a continuous lattice is a complete lattice in which is the smallest approximating auxiliary relation. The notions of the strong interpolation property and the interpolation property are also introduced.
منابع مشابه
Auxiliary and Approximating Relations
The aim of this paper is to formalize the second part of Chapter I Section 1 (1.9–1.19) in [12]. Definitions of Scott’s auxiliary and approximating relations are introduced in this work. We showed that in a meet-continuous lattice, the way-below relation is the intersection of all approximating auxiliary relations (proposition (40) — compare 1.13 in [12, pp. 43–47]). By (41) a continuous lattic...
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