6 found
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  1.  22
    Admissible Representations for Probability Measures.Matthias Schröder - 2007 - Mathematical Logic Quarterly 53 (4):431-445.
    In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type-2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical representation (...)
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  2.  7
    Computable Metrization.Tanja Grubba, Matthias Schröder & Klaus Weihrauch - 2007 - Mathematical Logic Quarterly 53 (4‐5):381-395.
    Every second-countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space can be considered computationally as a subspace of some computable metric space [15]. While Schröder's construction is “pointless”, i. e., only sets of a countable base but no concrete points are known, for a computable metric space a concrete dense set of computable points (...)
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  3.  9
    Addendum To: “The Bolzano–Weierstrass Theorem is the Jump of Weak Kőnig's Lemma” [Ann. Pure Appl. Logic 163 623–655].Vasco Brattka, Andrea Cettolo, Guido Gherardi, Alberto Marcone & Matthias Schröder - 2017 - Annals of Pure and Applied Logic 168 (8):1605-1608.
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  4.  10
    Editorial: Math. Log. Quart. 5/2008.Vasco Brattka, Hajime Ishihara, Matthias Schröder & Ning Zhong - 2008 - Mathematical Logic Quarterly 54 (5):453-453.
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  5.  7
    Spaces Allowing Type-2 Complexity Theory Revisited.Matthias Schröder - 2004 - Mathematical Logic Quarterly 50 (45):443-459.
    The basic concept of Type-2 Theory of Effectivity to define computability on topological spaces or limit spaces are representations, i. e. surjection functions from the Baire space onto X. Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type-2 Complexity Theory on the represented spaces. For each of these properties, we give a nice characterization of the (...)
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  6.  9
    Effectivity in Spaces with Admissible Multirepresentations.Matthias Schröder - 2002 - Mathematical Logic Quarterly 48 (S1):78-90.
    The property of admissibility of representations plays an important role in Type–2 Theory of Effectivity . TTE defines computability on sets with continuum cardinality via representations. Admissibility is known to be indispensable for guaranteeing reasonable effectivity properties of the used representations.The question arises whether every function that is computable with respect to arbritrary representations is also computable with respect to closely related admissible ones. We define three operators which transform representations into admissible ones in such a way that relative computability (...)
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