Saturated Filters at Successors of Singulars, Weak Reflection and Yet Another Weak Club Principle

@article{Damonja1996SaturatedFA,
  title={Saturated Filters at Successors of Singulars, Weak Reflection and Yet Another Weak Club Principle},
  author={Mirna D{\vz}amonja and Saharon Shelah},
  journal={Ann. Pure Appl. Log.},
  year={1996},
  volume={79},
  pages={289-316}
}

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References

SHOWING 1-10 OF 29 REFERENCES

Reflecting stationary sets and successors of singular cardinals

It is shown that supercompactness (and even the failure of PT) implies the existence of non-reflecting stationary sets, and that under suitable assumptions it is consistent that REF and there is a κ which is κ+n-supercompact.

Saturated ideals

  • K. Kunen
  • Mathematics
    Journal of Symbolic Logic
  • 1978
In this paper, we give consistency proofs for the existence of a κ-saturated ideal on an inaccessible κ, and for the existence of an ω2-saturated ideal on ω1. We also include an historical survey

A consistency result on weak reflection

In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say theta strongly non-reflects at lambda iff there is a function F: theta ---> lambda such that

Two consequences of determinacy consistent with choice

We begin with a ground model satisfying ZF + AD + ACR, and from it construct a generic extension satisfying ZFC + 6? = C2 + "the nonstationary ideal on coI is Co2-saturated". 0. Introduction. The

The generalized continuum hypothesis revisited

We can reformulate the generalized continuum problem as: for regular κ<λ we have λ to the power κ is λ, We argue that the reasonable reformulation of the generalized continuum hypothesis, considering

The consistency strength of “every stationary set reflects”

The consistency strength of a regular cardinal so that every stationary set reflects is the same as that of a regular cardinal with a normal idealI so that everyI-positive set reflects in aI-positive

A new class of order types

Advances in Cardinal Arithmetic

If cfκ = κ, κ + < cfλ = λ then there is a stationary subset S of {δ < λ : cf(δ) = κ} in I[λ]. Moreover, we can find C = 〈C δ : δ ∈ S〉, C δ club of λ, otp(C δ ) = κ, guessing clubs and for each α < λ

Cabal Seminar 79-81 : proceedings, Caltech-UCLA Logic Seminar 1979-81

More saturated ideals.- Some results in the wadge hierarchy of borel sets.- Pointclasses and well-ordered unions.- Ad and the uniqueness of the supercompact measures on P?1(?).- Scales on ? 1 1

Martin's Maximum, saturated ideals and non-regular ultrafilters. Part II

We prove, assuming the existence of a huge cardinal, the consistency of fully non-regular ultrafilters on the successor of any regular cardinal. We also construct ultrafilters with ultraproducts of