Nonregular ideals

  title={Nonregular ideals},
  author={Monroe Eskew},
  journal={arXiv: Logic},
Most of the regularity properties of ideals introduced by Taylor are equivalent at successor cardinals. For $\kappa = \mu^+$ with $\mathrm{cf}(\mu)$ uncountable, we can rid the universe of dense ideals on $\mathcal{P}_\kappa(\lambda)$ for while preserving nonregular ideals on the same set. 


Regularity properties of ideals and ultrafilters
Calculating quotient algebras of generic embeddings
Many consistency results in set theory involve forcing over a universe V0 that contains a large cardinal to get a model V1. The original large cardinal embedding is then extended generically using a
On cardinalities of ultraproducts
Introduction. In the theory of models, the ultraproduct (or prime reduced product) construction has been a very useful method of forming models with given properties (see, for instance, [2]). I t is
The extent of strength in the club filters
In this paper we consider whether the minimal normal filter onPκλ, the club filter, can have strong properties like saturation, pre-saturation, or cardinal preserving. We prove in a number of cases
Collapsing successors of singulars
Let κ be a singular cardinal in V , and let W ⊇ V be a model such that κ+V = λ + W for some W -cardinal λ with W |= cf(κ) 6= cf(λ). We apply Shelah’s pcf theory to study this situation, and prove the
Weak saturation properties of ideals
  • Infinite and finite sets,
  • 1975
Ideals and generic elementary embeddings, Handbook of set theory (Matthew
  • Foreman and Akihiro Kanamori, eds.),
  • 2010
Measurability Properties on Small Cardinals
Author(s): Eskew, Monroe Blake | Advisor(s): Zeman, Martin | Abstract: Ulam proved that there cannot exist a probability measure on the reals for which every set is measurable and gets either measure
Nonsplitting Subset of P (+)
  • M. Gitik
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1985