In this paper we show that there is no left adjoint to the inclusion functor from the full subcategory 𝒞0 of Scott domains (i.e., consistently complete ω–algebraic cpo's) to 𝒮ℱ𝒫, the category of 𝒮ℱ𝒫-objects and Scott-continuous maps. We also sho

Motivated by ideas from the study of abstract data types, the authors show how to interpret non-well-founded sets as fixed points of continuous transformations of an initial continuous algebra. They consider a preordered structure closely related to the set HF of well-founded, hereditarily finite sets. By taking its ideal completion, the authors obtain an initial continuous algebra in which they are able to solve all of the usual systems of equations that characterize hereditarily finite, non-well-founded sets. In this way, they are able to obtain a structure which is isomorphic to HF/sub 1/, the non-well-founded analog to HF.>

Article Free Access Share on Semantics for concurrency without powerdomains Author: F. J. Oles Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, New York Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, New YorkView Profile Authors Info & Claims POPL '87: Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languagesOctober 1987 Pages 211–222https://doi.org/10.1145/41625.41644Published:01 October 1987Publication History 4citation169DownloadsMetricsTotal Citations4Total Downloads169Last 12 Months9Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF