Here is the bibliography produced by my bibtex file.
A list of papers without summaries is also available.
The summaries given below are not necessarily the abstracts of the papers.
In the paper on PCF extended with real numbers, I had proposed to take affine maps as basic real number constructors. In this we propose to work with the larger monoid of Möbius transformations. This is possible because the information refinement property still holds. Again, we obtain a computationally adequate operational semantics. Advantages of generalizing affine maps to Möbius transformations are discussed in Peter Potts' and Abbas Edalat's papers available from their home pages.
Slides of a talk about this paper in Appsem'98.
Abstract: The lexicographical and numerical orders on infinite signed-digit numerals are unrelated. However, we show that there is a computable normalization operation on pairs of signed-digit numerals such that for normal pairs the two orderings coincide. In particular, one can always assume without loss of generality that any two numerals that denote the same number are themselves the same. We apply the order-normalization operator to easily obtain an effective and sequential definition-by-cases scheme in which the cases consist of inequalities between real numbers.
In order to avoid the ambiguous expression ``proper subspace embedding'', we refer to proper maps as finitary maps. We show that the finitary sober subspaces of the injective spaces are exactly the stably locally compact spaces. Moreover, the injective spaces over finitary embeddings are the algebras of the upper power space monad on the category of sober spaces. These coincide with the retracts of upper power spaces of sober spaces. In the full subcategory of locally compact sober spaces, these are known to be the continuous meet-semilattices. In the full subcategory of stably locally compact spaces these are again the continuous lattices.
The above characterization of the injective spaces over finitary embeddings is an instance of a general result on injective objects in poset-enriched categories with the structure of a KZ-monad established in this paper, which we also apply to various full subcategories closed under the upper power space construction and to the upper and lower power locale monads.
The above results also hold for the injective spaces over dense subspace embeddings (continuous Scott domains). Moreover, we show that every sober space has a smallest finitary dense sober subspace (its support ). The support always contains the subspace of maximal points, and in the stably locally compact case (which includes densely injective spaces) it is the subspace of maximal points iff that subspace is compact.
We relate our patch construction to Banaschewski and Brümmer's construction of the dual equivalence of the category of compact stably locally compact locales and perfect maps with the category of compact regular biframes and biframe homomorphisms.