10 found
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  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.  10
    Characterizations of Pretameness and the Ord-Cc.Peter Holy, Regula Krapf & Philipp Schlicht - 2018 - Annals of Pure and Applied Logic 169 (8):775-802.
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  3.  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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  4.  26
    A Minimal Prikry-Type Forcing for Singularizing a Measurable Cardinal.Peter Koepke, Karen Räsch & Philipp Schlicht - 2013 - Journal of Symbolic Logic 78 (1):85-100.
    Recently, Gitik, Kanovei and the first author proved that for a classical Prikry forcing extension the family of the intermediate models can be parametrized by $\mathscr{P}(\omega)/\mathrm{finite}$. By modifying the standard Prikry tree forcing we define a Prikry-type forcing which also singularizes a measurable cardinal but which is minimal, i.e., there are \emph{no} intermediate models properly between the ground model and the generic extension. The proof relies on combining the rigidity of the tree structure with indiscernibility arguments resulting from the normality (...)
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  5.  11
    Lipschitz and Uniformly Continuous Reducibilities on Ultrametric Polish Spaces.Philipp Schlicht & Motto Ros Luca - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 213-258.
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  6.  7
    Measurable Cardinals and Good Σ1-Wellorderings.Philipp Lücke & Philipp Schlicht - 2018 - Mathematical Logic Quarterly 64 (3):207-217.
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  7.  36
    Automata on Ordinals and Automaticity of Linear Orders.Philipp Schlicht & Frank Stephan - 2013 - Annals of Pure and Applied Logic 164 (5):523-527.
    We investigate structures recognizable by finite state automata with an input tape of length a limit ordinal. At limits, the set of states which appear unboundedly often before the limit are mapped to a limit state. We describe a method for proving non-automaticity and apply this to determine the optimal bounds for the ranks of linear orders recognized by such automata.
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  8.  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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  9.  5
    Continuous Reducibility and Dimension of Metric Spaces.Philipp Schlicht - 2018 - Archive for Mathematical Logic 57 (3-4):329-359.
    If is a Polish metric space of dimension 0, then by Wadge’s lemma, no more than two Borel subsets of X are incomparable with respect to continuous reducibility. In contrast, our main result shows that for any metric space of positive dimension, there are uncountably many Borel subsets of that are pairwise incomparable with respect to continuous reducibility. In general, the reducibility that is given by the collection of continuous functions on a topological space \\) is called the Wadge quasi-order (...)
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  10.  10
    Thin Equivalence Relations in Scaled Pointclasses.Ralf Schindler & Philipp Schlicht - 2011 - Mathematical Logic Quarterly 57 (6):615-620.
    For ordinals α beginning a Σ1 gap in equation image, where equation image is closed under number quantification, we give an inner model-theoretic proof that every thin equation image equivalence relation is equation image in a real parameter from the hypothesis equation image.
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