zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The largest Cartesian closed category of domains. (English) Zbl 0556.68017

Most of the studies in semantics of programming languages use ’domains’, i.e. ω-algebraic cpo’s; the corresponding category ω ACPO should be closed under function-space formation, reasonably. This is not true however. One does obtain Cartesian closure (the technical name of what we want) by considering the category ω ACPO-CC of consistently complete domains, but now the powerdomain construction takes us outside the category.

Plotkin has conjectured that the category SFP which is an extension of consistently complete domains while still a subcategory of that of domains (and which is closed under powerdomain and function-space formation) is the largest category of domains closed under the constructions aforementioned. The paper under review proves this, making extensive use of the set of finite elements of a domain and of the set of minimal bounds of a poset. Finally some extensions are considered in case the notion of ’domain’ is modified either to effectively given domains or to continuous domains: the author conjectures some of the results to be still true.

Reviewer: M.Eytan

MSC:
68Q99Theory of computing
18D15Closed categories
06B23Complete lattices, completions
68Q55Semantics