Margarita Korovina ; Oleg Kudinov - The Rice-Shapiro theorem in Computable Topology

lmcs:4171 - Logical Methods in Computer Science, December 29, 2017, Volume 13, Issue 4 - https://doi.org/10.23638/LMCS-13(4:30)2017
The Rice-Shapiro theorem in Computable Topology

Authors: Margarita Korovina ; Oleg Kudinov

    We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of effectively enumerable topological spaces where the Rice-Shapiro theorem does not hold. We propose two constructions that generate effectively enumerable topological spaces with particular properties from wn--families and computable trees without computable infinite paths. Using them we propose examples that give a flavor of this class.


    Volume: Volume 13, Issue 4
    Published on: December 29, 2017
    Accepted on: December 29, 2017
    Submitted on: December 29, 2017
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,03D45, 03D80

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