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  1. A degree-theoretic definition of the ramified analytical hierarchy.Carl G. Jockusch & Stephen G. Simpson - 1976 - Annals of Mathematical Logic 10 (1):1-32.
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  • Upper bounds for the arithmetical degrees.M. Lerman - 1985 - Annals of Pure and Applied Logic 29 (3):225-254.
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  • A fixed point for the jump operator on structures.Antonio Montalbán - 2013 - Journal of Symbolic Logic 78 (2):425-438.
    Assuming that $0^\#$ exists, we prove that there is a structure that can effectively interpret its own jump. In particular, we get a structure $\mathcal A$ such that \[ \textit{Sp}({\mathcal A}) = \{{\bf x}'\colon {\bf x}\in \textit{Sp}({\mathcal A})\}, \] where $\textit{Sp}({\mathcal A})$ is the set of Turing degrees which compute a copy of $\mathcal A$. More interesting than the result itself is its unexpected complexity. We prove that higher-order arithmetic, which is the union of full $n$th-order arithmetic for all $n$, (...)
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  • Finite level borel games and a problem concerning the jump hierarchy.Harold T. Hodes - 1984 - Journal of Symbolic Logic 49 (4):1301-1318.
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  • 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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