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1 results

  • ON SINGULAR STATIONARITY II (TIGHT STATIONARITY AND EXTENDERS-BASED METHODS)

  • OMER BEN-NERIA
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 1 / March 2019
    Published online by Cambridge University Press:
    14 March 2019, pp. 320-342
    Print publication:
    March 2019

  • We study the notion of tightly stationary sets which was introduced by Foreman and Magidor in [8]. We obtain two consistency results showing that certain sequences of regular cardinals ${\langle {\kappa _n}\rangle _{n < \omega }}$ can have the property that in some generic extension, every ground-model sequence of fixed-cofinality stationary sets ${S_n} \subseteq {\kappa _n}$ is tightly stationary. The results are obtained using variations of the short-extenders forcing method.