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Universal Profinite Domains
 Information and Computation
, 1987
"... . We introduce a bicartesian closed category of what we call profinite domains. Study of these domains is carried out through the use of an equivalent category of preorders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite dom ..."
Abstract

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. We introduce a bicartesian closed category of what we call profinite domains. Study of these domains is carried out through the use of an equivalent category of preorders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators. As a special instance of this construction, a universal domain for the category SFP is demonstrated. Necessary conditions for the existence of solutions for domain equations over the profinites are also given and used to derive results about solutions of some equations. A new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points. 1 Introduction. For our purposes a domain equation has the form X ΒΈ = F (X) where F is an operator on a class of semantic domains (typically, F is an endof...
The Classification of Continuous Domains (Extended Abstract)
"... Achim Jung y Technische Hochschule Darmstadt and Imperial College of Science and Technology, London Abstract The longstanding problem of finding the maximal cartesian closed categories of continuous domains is solved. The solution requires the definition of a new class of continuous domains, cal ..."
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Achim Jung y Technische Hochschule Darmstadt and Imperial College of Science and Technology, London Abstract The longstanding problem of finding the maximal cartesian closed categories of continuous domains is solved. The solution requires the definition of a new class of continuous domains, called FSdomains, which contains all retracts of SFPobjects. The properties of FSdomains are discussed in some detail. Keywords: continuous domains, SFPobjects, Lawsontopology, Smyth's Theorem, FSdomains, Ldomains 1 Introduction The first spaces suitable for the interpretation of programming language constructs were continuous lattices discovered by Dana Scott in the late sixties. Continuous lattices turned out to have numerous connections to other fields of mathematics such as algebra, topology, and convex analysis. An indication of this is the voluminous Bibliography of Continuous Lattices contained in [4]. In Computer Science, however, it was soon recognized that the subclass of al...