Representations of Algebraic Domains and Algebraic L-domains by Information Systems

Information systems play an important role in characterizing order structures. In this paper, we introduce the notions of the algebraic information system and algebraic L-information system. They are of the same logic-oriented style as the information system introduced by Scott (1982). But the axioms in this paper are briefer than reported in existing work. We also prove that the two new information systems exactly represent the algebraic domains and algebraic L-domains respectively. Based on the notion of approximable mapping between the algebraic information systems and the algebraic L-information systems, we obtain the result that the corresponding categories of algebraic information systems and algebraic L-information systems are equivalent to the category of algebraic domains and algebraic L-domains respectively.