Coherence and consistency in domains

Carl A. Gunter, Achim Jung

Research output: Contribution to journalArticle

Abstract

Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The goal of this paper is to explore the possibility of using a different condition - that of coherence - which has its origins in topology and logic. In particular, we concentrate on those posets whose principal ideals are algebraic lattices and whose topologies are coherent. These form a Cartesian closed category which has fixed points for domain equations. It is shown that a 'universal domain' exists. Since the construction of this domain seems to be of general significance, a categorical treatment is provided and applied to other classes of domains. Universal domains constructed in this fashion enjoy an additional property: they are saturated. We show that there is exactly one such domain in each of the classes under consideration.

Original languageEnglish (US)
Pages (from-to)49-66
Number of pages18
JournalJournal of Pure and Applied Algebra
Volume63
Issue number1
DOIs
StatePublished - Feb 23 1990
Externally publishedYes

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Algebraic Lattice
Cartesian Closed Category
Topology
Denotational Semantics
Poset
Categorical
Completeness
Fixed point
Logic
Class

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Coherence and consistency in domains. / Gunter, Carl A.; Jung, Achim.

In: Journal of Pure and Applied Algebra, Vol. 63, No. 1, 23.02.1990, p. 49-66.

Research output: Contribution to journalArticle

Gunter, Carl A. ; Jung, Achim. / Coherence and consistency in domains. In: Journal of Pure and Applied Algebra. 1990 ; Vol. 63, No. 1. pp. 49-66.
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