Weakly Distributive Domains

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 subcategory 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 I 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 dom...

• Type: Conference
• Year: 2007
• Where: TLCA
• Authors: Ying Jiang, Guo-Qiang Zhang
• Keywords: Cartesian Closed, Stable Functions, Theoretical Computer Science, TLCA 2007, ω-algebraic Meet-cpo