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Leo Harrington [23]Leo A. Harrington [7]
  1. On Σ1 Well-Orderings of the Universe.Leo Harrington & Thomas Jech - 1976 - Journal of Symbolic Logic 41 (1):167-170.
  2. A Mathematical Incompleteness in Peano Arithmetic.Jeff Paris & Leo Harrington - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 90--1133.
     
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  3.  34
    The D.R.E. Degrees Are Not Dense.S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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  4.  20
    Some Exact Equiconsistency Results in Set Theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
  5.  19
    The D.R.E. Degrees Are Not Dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
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  6.  31
    Analytic Determinacy and 0#. [REVIEW]Leo Harrington - 1978 - Journal of Symbolic Logic 43 (4):685 - 693.
  7.  16
    Fundamentals of Forking.Victor Harnik & Leo Harrington - 1984 - Annals of Pure and Applied Logic 26 (3):245-286.
  8. Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets.Leo Harrington & Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (2):199-213.
    We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of Felix Klein's Erlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and the Martin Invariance Conjecture on their Turing degrees, i.e., their information content with respect to relative computability (Turing reducibility).
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  9.  31
    On the Definability of the Double Jump in the Computably Enumerable Sets.Peter A. Cholak & Leo A. Harrington - 2002 - Journal of Mathematical Logic 2 (02):261-296.
    We show that the double jump is definable in the computably enumerable sets. Our main result is as follows: let [Formula: see text] is the Turing degree of a [Formula: see text] set J ≥T0″}. Let [Formula: see text] such that [Formula: see text] is upward closed in [Formula: see text]. Then there is an ℒ property [Formula: see text] such that [Formula: see text] if and only if there is an A where A ≡T F and [Formula: see text]. (...)
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  10.  7
    Recursively Presentable Prime Models.Leo Harrington - 1974 - Journal of Symbolic Logic 39 (2):305-309.
  11.  32
    Definable Properties of the Computably Enumerable Sets.Leo Harrington & Robert I. Soare - 1998 - Annals of Pure and Applied Logic 94 (1-3):97-125.
    Post in 1944 began studying properties of a computably enumerable set A such as simple, h-simple, and hh-simple, with the intent of finding a property guaranteeing incompleteness of A . From the observations of Post and Myhill , attention focused by the 1950s on properties definable in the inclusion ordering of c.e. subsets of ω, namely E = . In the 1950s and 1960s Tennenbaum, Martin, Yates, Sacks, Lachlan, Shoenfield and others produced a number of elegant results relating ∄-definable properties (...)
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  12.  15
    Codable Sets and Orbits of Computably Enumerable Sets.Leo Harrington & Robert I. Soare - 1998 - Journal of Symbolic Logic 63 (1):1-28.
    A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...)
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  13.  38
    The Complexity of Orbits of Computably Enumerable Sets.Peter A. Cholak, Rodney Downey & Leo A. Harrington - 2008 - Bulletin of Symbolic Logic 14 (1):69 - 87.
    The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...)
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  14.  2
    There is No Fat Orbit.Rod Downey & Leo Harrington - 1996 - Annals of Pure and Applied Logic 80 (3):277-289.
    We give a proof of a theorem of Harrington that there is no orbit of the lattice of recursively enumerable sets containing elements of each nonzero recursively enumerable degree. We also establish some degree theoretical extensions.
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  15.  34
    Models Without Indiscernibles.Fred G. Abramson & Leo A. Harrington - 1978 - Journal of Symbolic Logic 43 (3):572-600.
    For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size $\beth_n$ with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least $\beth_\omega$ . (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly $\beth_\omega$ ). If T ≠ true arithmetic, then $H(T) = \beth_{\omega1}$ . If $\delta \not\rightarrow (\rho)^{ , then any completion of (...)
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  16.  33
    Definable Encodings in the Computably Enumerable Sets.Peter A. Cholak & Leo A. Harrington - 2000 - Bulletin of Symbolic Logic 6 (2):185-196.
  17.  33
    Isomorphisms of Splits of Computably Enumerable Sets.Peter A. Cholak & Leo A. Harrington - 2003 - Journal of Symbolic Logic 68 (3):1044-1064.
    We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.
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  18.  2
    ℵ< Sub> 0-Categorical, ℵ< Sub> 0-Stable Structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
  19.  6
    Trivial Pursuit: Remarks on the Main Gap.John T. Baldwin & Leo Harrington - 1987 - Annals of Pure and Applied Logic 34 (3):209-230.
  20.  7
    Models and Types of Peano's Arithmetic.Haim Gaifman, Julia F. Knight, Fred G. Abramson & Leo A. Harrington - 1983 - Journal of Symbolic Logic 48 (2):484-485.
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  21.  7
    Corrigendum to “The D.R.E. Degrees Are Not Dense” [Ann. Pure Appl. Logic 55 (1991) 125–151].S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 2017 - Annals of Pure and Applied Logic 168 (12):2164-2165.
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  22.  7
    On $Sigma_1$ Well-Orderings of the Universe.Leo Harrington & Thomas Jech - 1976 - Journal of Symbolic Logic 41 (1):167-170.
  23.  8
    On Characterizing Spector Classes.Leo A. Harrington & Alexander S. Kechris - 1975 - Journal of Symbolic Logic 40 (1):19-24.
  24.  5
    Meeting of the Association for Symbolic Logic: Reno, 1976.Solomon Feferman, Jon Barwise & Leo Harrington - 1977 - Journal of Symbolic Logic 42 (1):156-160.
  25. University of Illinois at Chicago, Chicago, IL, June 1–4, 2003.Gregory Cherlin, Alan Dow, Yuri Gurevich, Leo Harrington, Ulrich Kohlenbach, Phokion Kolaitis, Leonid Levin, Michael Makkai, Ralph McKenzie & Don Pigozzi - 2004 - Bulletin of Symbolic Logic 10 (1).
     
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