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Journal of Logic and Computation 1992 2(2):119-131; doi:10.1093/logcom/2.2.119
© 1992 by Oxford University Press
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Original Articles

Finite Axiomatizations for Universal Domains

MANFRED DROSTE

Fb 6-Mathematik und Informatik, Universität GHS Essen D-4300 Essen 1, Germany

In the theory of denotational semantics of programming languages, several authors established the existence of particular kinds of universal domains. Here we consider the categories of all {omega}-bifinite domain, all {omega}-bifinite L-domains, all {omega}-Scott-domains, and all {omega}-algebraic lattices, respectively, in each case with embedding-projection pairs as morphisms. It has been shown that each of these categories contains a universal homogeneous, or saturated. object. which is unipue up to isomorphism. Here we introduce for each of these four categories l a finite set of axioms Sl, formulated in a first-order language of predicate calculus for posets, and show that an arbitrary domain (D, ≤){varepsilon} l is the universal homogeneous object in l if and only if its subset of compact elements satisfies all axioms in Sl.

Keywords: Universal domain; denotational semantics; Scott-domain; bifinite domain; L-domain; finite axiomatizability


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