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  1. Hyperarithmetical relations in expansions of recursive structures.Alan D. Vlach - 1994 - Annals of Pure and Applied Logic 66 (2):163-196.
    Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a recursive (...)
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  • The Galvin-Prikry theorem and set existen axioms.Kazuyuki Tanaka - 1989 - Annals of Pure and Applied Logic 42 (1):81-104.
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  • Periodic points and subsystems of second-order arithmetic.Harvey Friedman, Stephen G. Simpson & Xiaokang Yu - 1993 - Annals of Pure and Applied Logic 62 (1):51-64.
    We study the formalization within sybsystems of second-order arithmetic of theorems concerning periodic points in dynamical systems on the real line. We show that Sharkovsky's theorem is provable in WKL0. We show that, with an additional assumption, Sharkovsky's theorem is provable in RCA0. We show that the existence for all n of n-fold iterates of continuous mappings of the closed unit interval into itself is equivalent to the disjunction of Σ02 induction and weak König's lemma.
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