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  1. Computability of Measurable Sets Via Effective Topologies.Yongcheng Wu & Decheng Ding - 2005 - Archive for Mathematical Logic 45 (3):365-379.
    We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite computable measure space, and analyze the computability of the considered functions via respectively each of the standard representations of the computable topological spaces (...)
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  • Computable Symbolic Dynamics.Douglas Cenzer, S. Ali Dashti & Jonathan L. F. King - 2008 - Mathematical Logic Quarterly 54 (5):460-469.
    We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2ℕ to 2ℕ such that P is the set of itineraries of elements of 2ℕ. Π01 subshifts are constructed in 2ℕ and in 2ℤ which have no computable elements. We also consider the symbolic dynamics of maps on the unit interval.
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