Paul Taylor

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We present an elementary axiomatisation of synthetic domain theory and show that it is sufficient to deduce the fixed point property and solve domain equations. Models of these axioms based on partial equivalence relations have received much attention, but there are also very simple sheaf models based on classical domain theory. In any case the aim of this(More)
Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction. However these ordinals are not directed and their successor operation is poorly behaved, leading to problems of functoriality. We show how to make the successor monotone by introducing plumpness, which strengthens transitivity. This(More)
The first paper published on Abstract Stone Duality showed that the overt discrete objects (those admitting ∃ and = internally) form a pretopos, i.e. a category with finite limits, stable disjoint coproducts and stable effective quotients of equivalence relations. Using an N-indexed least fixed point axiom, here we show that this full subcategory is an(More)
One of the objectives of category theory is to provide a foundation for itself in particular and mathematics in general which is independent of the traditional use of set theory. A major question in this programme is how to formulate the fact that Set is " complete " , i.e. it has all " small " (i.e. set-rather than class-indexed) limits (and colimits). The(More)
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