Filters and Large Cardinals

  title={Filters and Large Cardinals},
  author={Jean-Pierre Levinski},
  journal={Ann. Pure Appl. Logic},
Assuming the consistency of the theory “ZF’C + there exists a measurable cardinal”, we construct (1) a model in which the first cardinal ti, such that 2” > tit, bears a normal filter F whose associated boolean algebra is K+ -distributive (and indeed strongly K+-distributive as defined in Section 5), (2) a model where there is a measurable cardinal K such that, for every regular cardinal p -=z ti, 2p = p ’ + holds, (3) a model of “ZFC + GCH” where there exists a non-measurable cardinal K bearing… CONTINUE READING