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Search results for 'Christopher P. Alfeld' (try it on Scholar)

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  1. Christopher P. Alfeld (2008). Classifying the Branching Degrees in the Medvedev Lattice of $\Pi^0_1$ Classes. Notre Dame Journal of Formal Logic 49 (3):227-243.score: 960.0
    A $\Pi^0_1$ class can be defined as the set of infinite paths through a computable tree. For classes $P$ and $Q$, say that $P$ is Medvedev reducible to $Q$, $P \leq_M Q$, if there is a computably continuous functional mapping $Q$ into $P$. Let $\mathcal{L}_M$ be the lattice of degrees formed by $\Pi^0_1$ subclasses of $2^\omega$ under the Medvedev reducibility. In "Non-branching degrees in the Medvedev lattice of $\Pi \sp{0}\sb{1} classes," I provided a characterization of nonbranching/branching and a classification of (...)
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  2. Christopher P. Alfeld (2007). Non-Branching Degrees in the Medvedev Lattice of [Image] Classes. Journal of Symbolic Logic 72 (1):81 - 97.score: 960.0
    A $\Pi _{1}^{0}$ class is the set of paths through a computable tree. Given classes P and Q, P is Medvedev reducible to Q, P ≤M Q, if there is a computably continuous functional mapping Q into P. We look at the lattice formed by $\Pi _{1}^{0}$ subclasses of 2ω under this reduction. It is known that the degree of a splitting class of c.e. sets is non-branching. We further characterize non-branching degrees, providing two additional properties which guarantee non-branching: inseparable (...)
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