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Timothy H. McNicholl [12]Timothy McNicholl [6]
  1.  46
    Reverse Mathematics, Computability, and Partitions of Trees.Jennifer Chubb, Jeffry L. Hirst & Timothy H. McNicholl - 2009 - Journal of Symbolic Logic 74 (1):201-215.
    We examine the reverse mathematics and computability theory of a form of Ramsey's theorem in which the linear n-tuples of a binary tree are colored.
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  2.  12
    Asymptotic Density and the Ershov Hierarchy.Rod Downey, Carl Jockusch, Timothy H. McNicholl & Paul Schupp - 2015 - Mathematical Logic Quarterly 61 (3):189-195.
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  3.  27
    $\pi _{1}^{0}$ Classes and Strong Degree Spectra of Relations.John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denis R. Hirschfeldt, Carl G. Jockusch, Timothy McNicholl & Sarah Pingrey - 2007 - Journal of Symbolic Logic 72 (3):1003 - 1018.
    We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable $\Pi _{1}^{0}$ subsets of 2ω and Kolmogorov complexity play a major role in the proof.
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  4.  54
    The Complexity of Oddan.Richard Beigel, William Gasarch, Martin Kummer, Georgia Martin, Timothy McNicholl & Frank Stephan - 2000 - Journal of Symbolic Logic 65 (1):1 - 18.
    For a fixed set A, the number of queries to A needed in order to decide a set S is a measure of S's complexity. We consider the complexity of certain sets defined in terms of A: $ODD^A_n = \{(x_1, \dots ,x_n): {\tt\#}^A_n(x_1, \dots, x_n) \text{is odd}\}$ and, for m ≥ 2, $\text{MOD}m^A_n = \{(x_1, \dots ,x_n):{\tt\#}^A_n(x_1, \dots ,x_n) \not\equiv 0 (\text{mod} m)\},$ where ${\tt\#}^A_n(x_1, \dots ,x_n) = A(x_1)+\cdots+A(x_n)$ . (We identify A(x) with χ A (x), where χ A is (...)
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  5.  15
    The Complexity of ODDnA.Richard Beigel, William Gasarch, Martin Kummer, Georgia Martin, Timothy Mcnicholl & Frank Stephan - 2000 - Journal of Symbolic Logic 65 (1):1-18.
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  6.  26
    On the Convergence of Query-Bounded Computations and Logical Closure Properties of C.E. Sets.Timothy H. McNicholl - 2001 - Journal of Symbolic Logic 66 (4):1543-1560.
    Call a set A n-correctable if every set Turing reducible to A via a Turing machine that on any input makes at most n queries is Turing reducible to A via a Turing machine that on any input makes at most n-queries and on any input halts no matter what answers are given to its queries. We show that if a c.e. set A is n-correctable for some n ≥ 2, then it is n-correctable for all n. We show that (...)
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  7.  21
    A Uniformly Computable Implicit Function Theorem.Timothy H. McNicholl - 2008 - Mathematical Logic Quarterly 54 (3):272-279.
    We prove uniformly computable versions of the Implicit Function Theorem in its differentiable and non-differentiable forms. We show that the resulting operators are not computable if information about some of the partial derivatives of the implicitly defining function is omitted. Finally, as a corollary, we obtain a uniformly computable Inverse Function Theorem, first proven by M. Ziegler.
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  8.  19
    On the Commutativity of Jumps.Timothy H. McNicholl - 2000 - Journal of Symbolic Logic 65 (4):1725-1748.
    We study the following classes: Q* (r 1 A 1 ,..., r kA k ) which is defined to be the collection of all sets that can be computed by a Turing machine that on any input makes a total of r i queries to A i for all i ∈ {1,..., k}. Q(r 1A 1 ,...,r kA k ) which is defined like Q* (r 1A 1 ,..., r kA k ) except that queries to A i must be (...)
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  9.  19
    Computing Links and Accessing Arcs.Timothy H. McNicholl - 2013 - Mathematical Logic Quarterly 59 (1-2):101-107.
    Sufficient conditions are given for the computation of an arc that accesses a point on the boundary of an open subset of the plane from a point within the set. The existence of a not-computably-accessible but computable point on a computably compact arc is also demonstrated.
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  10.  4
    On the Complexity of Classifying Lebesgue Spaces.Tyler A. Brown, Timothy H. Mcnicholl & Alexander G. Melnikov - 2020 - Journal of Symbolic Logic 85 (3):1254-1288.
    Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.
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  11.  11
    Effective Embeddings Into Strong Degree Structures.Timothy H. McNicholl - 2003 - Mathematical Logic Quarterly 49 (3):219.
    We show that any partial order with a Σ3 enumeration can be effectively embedded into any partial order obtained by imposing a strong reducibility such as ≤tt on the c. e. sets. As a consequence, we obtain that the partial orders that result from imposing a strong reducibility on the sets in a level of the Ershov hiearchy below ω + 1 are co-embeddable.
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  12.  12
    Uniformly Computable Aspects of Inner Functions: Estimation and Factorization.Timothy H. McNicholl - 2008 - Mathematical Logic Quarterly 54 (5):508-518.
    The theory of inner functions plays an important role in the study of bounded analytic functions. Inner functions are also useful in applied mathematics. Two foundational results in this theory are Frostman's Theorem and the Factorization Theorem. We prove a uniformly computable version of Frostman's Theorem. We then show that the Factorization Theorem is not uniformly computably true. We then show that for an inner function u with infinitely many zeros, the Blaschke sum of u provides the exact amount of (...)
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  13.  4
    Analytic Computable Structure Theory and $$L^P$$Lp -Spaces Part 2.Tyler Brown & Timothy H. McNicholl - 2020 - Archive for Mathematical Logic 59 (3-4):427-443.
    Suppose \ is a computable real. We extend previous work of Clanin, Stull, and McNicholl by determining the degrees of categoricity of the separable \ spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we ascertain the complexity of associated projection maps.
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  14.  24
    Intrinsic Reducibilities.Timothy H. McNicholl - 2000 - Mathematical Logic Quarterly 46 (3):393-407.
    Let equation image. We show that for many reducibilities, the requirement that a relation be intrinsically reducible to the α-th jump of a countable mode A has a syntactic equivalent. Furthermore, we show that many reducibilities coincide in such a situation.
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  15.  1
    Continuous Logic and Embeddings of Lebesgue Spaces.Timothy H. McNicholl - 2021 - Archive for Mathematical Logic 60 (1-2):105-119.
    We use the compactness theorem of continuous logic to give a new proof that Lr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^r$$\end{document} isometrically embeds into Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} whenever 1≤p≤r≤2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 \le p \le r \le 2$$\end{document}. We will also give a proof for the complex case. This will involve a new characterization of complex Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} (...)
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