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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 its relationship to other applications discussed.
Carl A. Gunter and Achim Jung, "Coherence and Consistency in Domains (Extended Outline)", . March 1988.
Date Posted: 21 September 2007