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  1. On a Convenient Property About $${[\Gamma]^{\Aleph_0}}$$.David Asperó - 2009 - Archive for Mathematical Logic 48 (7):653-677.
    Several situations are presented in which there is an ordinal γ such that ${\{ X \in [\gamma]^{\aleph_0} : X \cap \omega_1 \in S\,{\rm and}\, ot(X) \in T \}}$ is a stationary subset of ${[\gamma]^{\aleph_0}}$ for all stationary ${S, T\subseteq \omega_1}$ . A natural strengthening of the existence of an ordinal γ for which the above conclusion holds lies, in terms of consistency strength, between the existence of the sharp of ${H_{\omega_2}}$ and the existence of sharps for all reals. Also, an (...)
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  • Coding by Club-Sequences.David Asperó - 2006 - Annals of Pure and Applied Logic 142 (1):98-114.
    Given any subset A of ω1 there is a proper partial order which forces that the predicate xA and the predicate xω1A can be expressed by -provably incompatible Σ3 formulas over the structure Hω2,,NSω1. Also, if there is an inaccessible cardinal, then there is a proper partial order which forces the existence of a well-order of Hω2 definable over Hω2,,NSω1 by a provably antisymmetric Σ3 formula with two free variables. The proofs of these results involve a technique for manipulating the (...)
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