Theoretical Computer Science
Logic of domains
Theoretical Computer Science - Special volume of selected papers of the Sixth Workshop on the Mathematical Foundations of Programming Semantics, Kingston, Ont., Canada, May 1990
dI-Domains as prime information systems
Information and Computation
The largest cartesian closed category of stable domains
Theoretical Computer Science
DI-Domains as a Model of Polymorphism
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
An introduction to event structures
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
Proceedings of the 4th International Conference on Category Theory and Computer Science
Domains and Lambda-Calculi (Cambridge Tracts in Theoretical Computer Science)
Domains and Lambda-Calculi (Cambridge Tracts in Theoretical Computer Science)
On an open problem of Amadio and Curien: The finite antichain condition
Information and Computation
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In our previous work [17] we have shown that for any ω-algebraic meet-cpo D, if all higher-order stable function spaces built from D are ω-algebraic, then D is finitary. This accomplishes the first of a possible, two-step process in solving the problem raised in [1,2]: whether the category of stable bifinite domains of Amadio-Droste-Göbel [1,6] is the largest cartesian closed full sub-category within the category of ω-algebraic meet-cpos with stable functions. This paper presents results on the second step, which is to show that for any ω-algebraic meet-cpo D satisfying axioms M and | to be contained in a cartesian closed full sub-category using ω-algebraic meet-cpos with stable functions, it must not violate MI∞. We introduce a new class of domains called weakly distributive domains and show that for these domains to be in a cartesian closed category using ω-algebraic meet-cpos, property MI∞ must not be violated. We further demonstrate that principally distributive domains (those for which each principle ideal is distributive) form a proper subclass of weakly distributive domains, and Birkhoff's M3 and N5 [5] are weakly distributive (but non-distributive). We introduce also the notion of meet-generators in constructing stable functions and show that if an ω-algebraic meet-cpo D contains an infinite number of meet-generators, then [D → D] fails I. However, the original problem of Amadio and Curien remains open.