Regularity properties of ideals and ultrafilters

@article{Taylor1979RegularityPO,
  title={Regularity properties of ideals and ultrafilters},
  author={Alan D. Taylor},
  journal={Annals of Mathematical Logic},
  year={1979},
  volume={16},
  pages={33-55}
}
  • Alan D. Taylor
  • Published 1 May 1979
  • Mathematics
  • Annals of Mathematical Logic

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Abstract Let κ denote a regular uncountable cardinal and NS the normal ideal of nonstationary subsets of κ. Our results concern the well-known open question whether NS fails to be κ+-saturated, i.e.,

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We prove that if Kurepa's Hypothesis holds, then on a set of cardinality ℵ1, there does not exist a family of ℵ1 non-trivial measures such that each subset is measurable with respect to at least one

Regularity of ultrafilters

If there arek++ eventually functions fromk+ intok or if there arek++ eventually different functions fromk+ then uniform ultrafilters onk+ are (k, k+)-regular.

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We can characterize the real line, up to order isomorphism, by the following list of properties: R is order complete, order dense, has no first or last elements, and contains a countable dense

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