Article ID Journal Published Year Pages File Type
422810 Electronic Notes in Theoretical Computer Science 2014 10 Pages PDF
Abstract

In this paper, concepts of strongly way below relations, completely precontinuous posets, coprimes and Heyting posets are introduced. The main results are: (1) The strongly way below relations of completely precontinuous posets have the interpolation property; (2) A poset P is a completely precontinuous poset iff its normal completion is a completely distributive lattice; (3) An ω-chain complete P is completely precontinuous iff P and Pop are precontinuous and its normal completion is distributive iff P is precontinuous and has enough coprimes; (4) A poset P is completely precontinuous iff the strongly way below relation is the smallest approximating auxiliary relation on P iff P is a Heyting poset and there is a smallest approximating auxiliary relation on P. Finally, given a poset P and an auxiliary relation on P, we characterize those join-dense subsets of P whose strongly way-below relation agrees with the given auxiliary relation.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics