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Applications of the KleeneKreisel Density Theorem to Theoretical Computer Science
, 2006
"... The KleeneKreisel density theorem is one of the tools used to investigate the denotational semantics of programs involving higher types. We give a brief introduction to the classical density theorem, then show how this may be generalized to set theoretical models for algorithms accepting real numbe ..."
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The KleeneKreisel density theorem is one of the tools used to investigate the denotational semantics of programs involving higher types. We give a brief introduction to the classical density theorem, then show how this may be generalized to set theoretical models for algorithms accepting real numbers as inputs and finally survey some recent applications of this generalization. 1
Definability and reducibility in higher types over the reals
 the proceedings of Logic Colloquium ’03
"... We consider sets CtR(σ) of total, continuous functionals of type σ over the reals. A subset A ⊆ CtR(σ) is reducible if A can be reduced to totality in one of the other spaces. We show that all Polish spaces are homeomorphic to a reducible subset of R → R and that the class of reducible sets is close ..."
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We consider sets CtR(σ) of total, continuous functionals of type σ over the reals. A subset A ⊆ CtR(σ) is reducible if A can be reduced to totality in one of the other spaces. We show that all Polish spaces are homeomorphic to a reducible subset of R → R and that the class of reducible sets is closed under the formation of function spaces and some comprehension. 1
Cantor–Weihrauch domain representations
, 2007
"... We hope you have now downloaded a proof of your paper in pdf format, and also the Transfer of ..."
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We hope you have now downloaded a proof of your paper in pdf format, and also the Transfer of
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, 2003
"... Definability and reducibility in higher types over the reals ..."
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Mathematical Logic Quarterly
"... Abstract. In this paper I compare two well studied approaches to topological semantics— ..."
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Abstract. In this paper I compare two well studied approaches to topological semantics—
Admissible Domain Representations of Convergence Spaces
"... In this paper we consider admissible domain representations of convergence spaces. A convergence space is a pair (X, →X) where X is a set and →X is a binary relation between nets on X and elements of X. We study in particular the case when (X, →X) is a weak κconvergence space, which roughly means t ..."
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In this paper we consider admissible domain representations of convergence spaces. A convergence space is a pair (X, →X) where X is a set and →X is a binary relation between nets on X and elements of X. We study in particular the case when (X, →X) is a weak κconvergence space, which roughly means that →X is a relation satisfying a generalisation of the Kuratowski limit axioms to cardinality κ. As a framework for our study of weak κconvergence spaces and the related class of weak convergence spaces we use admissible domain representations. A domain representation D of a space X is λadmissible if, in principle, all other λbased domain representations E of X can be reduced to D via a continuous function from E to D. We present two major results. First we show that the category of weak κconvergence spaces is cartesian closed. The second result is that the category of weak κconvergence spaces that have a dense, λadmissible, κcontinuous and αbased consistently complete domain representation is cartesian closed when α ≤ λ ≥ κ, thus generalising the results of [Sch01]. As natural corollaries we obtain corresponding results for weak convergence spaces. 1