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  1. Peter A. Cholak, Rodney Downey & Leo A. Harrington (2008). The Complexity of Orbits of Computably Enumerable Sets. 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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  2. Peter A. Cholak & Leo A. Harrington (2003). Isomorphisms of Splits of Computably Enumerable Sets. 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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  3. Peter A. Cholak & Leo A. Harrington (2002). On the Definability of the Double Jump in the Computably Enumerable Sets. Journal of Mathematical Logic 2 (02):261-296.
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  4. Peter A. Cholak & Leo A. Harrington (2000). Definable Encodings in the Computably Enumerable Sets. Bulletin of Symbolic Logic 6 (2):185-196.
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  5. Leo A. Harrington & Alexander S. Kechris (1981). On the Determinacy of Games on Ordinals. Annals of Mathematical Logic 20 (2):109-154.
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  6. Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. 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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  7. Leo A. Harrington & Alexander S. Kechris (1975). On Characterizing Spector Classes. Journal of Symbolic Logic 40 (1):19-24.
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