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Universal domains and the amalgamation property†

Published online by Cambridge University Press:  04 March 2009

Manfred Droste  and
Rüdiger Gübel
Manfred Droste
Affiliation:
Fb 6 – Mathematik und Informatik, Universität GHS Essen, D-4300 Essen 1, Germany
Rüdiger Gübel
Affiliation:
Fb 6 – Mathematik und Informatik, Universität GHS Essen, D-4300 Essen 1, Germany
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Abstract

In the theory of denotational semantics of programming languages, several authors have constructed various kinds of universal domains. We present here a categorical generalization of a well-known result in model theory, which we use to characterize large classes of reasonable categories that contain universal homogeneous objects. The existence of such objects is characterized by the condition that the finite objects in the category satisfy the amalgamation property. We derive from this the existence and uniqueness of universal homogeneous domains for several categories of bifinite domains, with embedding-projection-pairs as morphisms. We also obtain universal homogeneous objects for various categories of stable bifinite domains. In contrast, several categories of event domains and concrete domains and the category of all coherent Scott-domains do not contain universal homogeneous objects. Finally, we show that all our constructions can be performed effectively.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 3 , Issue 2 , June 1993 , pp. 137 - 159
Copyright
Copyright © Cambridge University Press 1993

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