1.  6
    Infinite Computations with Random Oracles.Merlin Carl & Philipp Schlicht - 2017 - Notre Dame Journal of Formal Logic 58 (2):249-270.
    We consider the following problem for various infinite-time machines. If a real is computable relative to a large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it already computable? We show that the answer is independent of ZFC for ordinal Turing machines with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite-time Turing machines, unresetting and (...)
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  2.  12
    Recognizable Sets and Woodin Cardinals: Computation Beyond the Constructible Universe.Merlin Carl, Philipp Schlicht & Philip Welch - 2018 - Annals of Pure and Applied Logic 169 (4):312-332.
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  3.  31
    The Basic Theory of Infinite Time Register Machines.Merlin Carl, Tim Fischbach, Peter Koepke, Russell Miller, Miriam Nasfi & Gregor Weckbecker - 2010 - Archive for Mathematical Logic 49 (2):249-273.
    Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times register contents are defined by appropriate limit operations. In this paper, we examine the ITRMs introduced by the third and fourth author (Koepke and Miller in Logic and Theory of Algorithms LNCS, pp. 306–315, 2008), where a register content at a limit time is set (...)
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  4.  5
    Randomness Via Infinite Computation and Effective Descriptive Set Theory.Merlin Carl & Philipp Schlicht - 2018 - Journal of Symbolic Logic 83 (2):766-789.
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    Optimal Results on Recognizability for Infinite Time Register Machines.Merlin Carl - 2015 - Journal of Symbolic Logic 80 (4):1116-1130.