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  1. Compactness and guessing principles in the Radin extensions.Omer Ben-Neria & Jing Zhang - 2023 - Journal of Mathematical Logic 23 (2).
    We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on [Formula: see text], if [Formula: see text] is weakly compact, then [Formula: see text] holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the diamond principle fails (...)
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  • ◇ at Mahlo cardinals.Martin Zeman - 2000 - Journal of Symbolic Logic 65 (4):1813-1822.
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  • Diamond (on the regulars) can fail at any strongly unfoldable cardinal.Mirna Džamonja & Joel David Hamkins - 2006 - Annals of Pure and Applied Logic 144 (1-3):83-95.
    If κ is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which κ fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser.
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  • Diamonds, compactness, and measure sequences.Omer Ben-Neria - 2019 - Journal of Mathematical Logic 19 (1):1950002.
    We establish the consistency of the failure of the diamond principle on a cardinal [Formula: see text] which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of [Formula: see text] in a Radin generic extension.
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