6 found
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  1.  14
    Bounded Low and High Sets.Bernard A. Anderson, Barbara F. Csima & Karen M. Lange - 2017 - Archive for Mathematical Logic 56 (5-6):507-521.
    Anderson and Csima :245–264, 2014) defined a jump operator, the bounded jump, with respect to bounded Turing reducibility. They showed that the bounded jump is closely related to the Ershov hierarchy and that it satisfies an analogue of Shoenfield jump inversion. We show that there are high bounded low sets and low bounded high sets. Thus, the information coded in the bounded jump is quite different from that of the standard jump. We also consider whether the analogue of the Jump (...)
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  2.  27
    Automorphisms of the Truth-Table Degrees Are Fixed on a Cone.Bernard A. Anderson - 2009 - Journal of Symbolic Logic 74 (2):679-688.
    Let $D_{tt} $ denote the set of truth-table degrees. A bijection π: $D_{tt} \to \,D_{tt} $ is an automorphism if for all truth-table degrees x and y we have $ \leqslant _{tt} \,y\, \Leftrightarrow \,\pi (x)\, \leqslant _{tt} \,\pi (y)$ . We say an automorphism π is fixed on a cone if there is a degree b such that for all $x \geqslant _{tt} b$ we have π(x) = x. We first prove that for every 2-generic real X we have (...)
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  3.  33
    Relatively Computably Enumerable Reals.Bernard A. Anderson - 2011 - Archive for Mathematical Logic 50 (3-4):361-365.
    A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and ${X \not\leq_T Y}$ . A real X is relatively simple and above if there is a real Y < T X such that X is c.e.(Y) and there is no infinite set ${Z \subseteq \overline{X}}$ such that Z is c.e.(Y). We prove that every nonempty ${\Pi^0_1}$ class contains a member which is not relatively c.e. and that every 1-generic real (...)
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  4.  26
    Partitions of Trees and $${{\sf ACA}^\prime_{0}}$$.Bernard A. Anderson & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (3-4):227-230.
    We show that a version of Ramsey’s theorem for trees for arbitrary exponents is equivalent to the subsystem ${{\sf ACA}^\prime_{0}}$ of reverse mathematics.
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  5.  20
    Partitions of Trees And.Bernard A. Anderson & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (3-4):227-230.
    We show that a version of Ramsey’s theorem for trees for arbitrary exponents is equivalent to the subsystem \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\sf ACA}^\prime_{0}}$$\end{document} of reverse mathematics.
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  6.  20
    Reals N-Generic Relative to Some Perfect Tree.Bernard A. Anderson - 2008 - Journal of Symbolic Logic 73 (2):401 - 411.
    We say that a real X is n-generic relative to a perfect tree T if X is a path through T and for all $\Sigma _{n}^{0}(T)$ sets S, there exists a number k such that either X|k ∈ S or for all σ ∈ T extending X|k we have σ ∉ S. A real X is n-generic relative to some perfect tree if there exists such a T. We first show that for every number n all but countably many reals (...)
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