Switch to: References

Citations of:

$\Diamond$ at mahlo cardinals

Journal of Symbolic Logic 65 (4):1813 - 1822 (2000)

Add citations

You must login to add citations.
  1. Guessing more sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark