10.4230/OASICS.CCA.2009.2252
Scott, Dana
Dana
Scott
Semilattices, Domains, and Computability (Invited Talk)
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2009
Invited Talk
Semilattices
domains
computability
Bauer, Andrej
Andrej
Bauer
Hertling, Peter
Peter
Hertling
Ko, Ker-I
Ker-I
Ko
2009
2009-11-25
2009-11-25
2009-11-25
en
urn:nbn:de:0030-drops-22525
10.4230/OASIcs.CCA.2009
978-3-939897-12-5
2190-6807
10.4230/OASIcs.CCA.2009
OASIcs, Volume 11, CCA 2009
6th International Conference on Computability and Complexity in Analysis (CCA'09)
2012
11
4
17
17
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Bauer, Andrej
Andrej
Bauer
Hertling, Peter
Peter
Hertling
Ko, Ker-I
Ker-I
Ko
2190-6807
Open Access Series in Informatics (OASIcs)
2009
11
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
1 pages
103092 bytes
application/pdf
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
As everyone knows, one popular notion of Scott domain is defined as a bounded complete algebraic cpo. These are closely related to algebraic lattices: (i) A Scott domain becomes an algebraic lattice with the adjunction of an (isolated) top element. (ii) Every non-empty Scott-closed subset of an algebraic lattice is a Scott domain. Moreover, the isolated ($=$ compact) elements of an algebraic lattice form a semilattice (under join). This semilattice has a zero element, and, provided the top element is isolated, it also has a unit element. The algebraic lattice itself may be regarded as the ideal completion of the semilattice of isolated elements. This is all well known. What is not so clear that is that there is an easy-to-construct domain of countable semilattices giving isomorphic copies of all countably based domains. This approach seems to have advantages over both ``information systems'' or more abstract lattice formulations, and it makes definitions of solutions to domain equations very elementary to justify. The ``domain of domains'' also has an immediate computable structure.
OASIcs, Vol. 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09), pages 17-17