Nonregular ideals

@article{Eskew2019NonregularI,
  title={Nonregular ideals},
  author={Monroe Eskew},
  journal={arXiv: Logic},
  year={2019}
}
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. 
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References

SHOWING 1-10 OF 14 REFERENCES
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…
Mutually stationary sequences of sets and the non-saturation of the non-stationary ideal onPϰ(λ)
Nonsplitting Subset of P (+)
  • M. Gitik
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1985
...
...