A characterization of the consistent Hoare powerdomains over dcpos
pith:CHATML4E Add to your LaTeX paper
What is a Pith Number?\usepackage{pith}
\pithnumber{CHATML4E}
Prints a linked pith:CHATML4E badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more
read the original abstract
It has been shown that for a dcpo P, the Scott closure of \Gamma_c(P) in \Gamma(P) is a consistent Hoare powerdomain of P, where \Gamma_c(P) is the family of nonempty, consistent and Scott closed subsets of P, and \Gamma(P) is the collection of all nonempty Scott closed subsets of P. In this paper, by introducing the notion of a \vee-existing set, we present a direct characterization of the consistent Hoare powerdomain: the set of all \vee-existing Scott closed subsets of a dcpo P is exactly the consistent Hoare powerdomain of P. We also introduce the concept of an F-Scott closed set over each dcpo-\vee-semilattice. We prove that the Scott closed set lattice of a dcpo P is isomorphic to the family of all F-Scott closed sets of P's consistent Hoare powerdomain.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.