More rigid ideals

@article{Eskew2019MoreRI,
  title={More rigid ideals},
  author={Monroe Eskew},
  journal={Israel Journal of Mathematics},
  year={2019}
}
  • Monroe Eskew
  • Published 4 January 2019
  • Mathematics
  • Israel Journal of Mathematics
We extend prior results of Cody-Eskew, showing the consistency of GCH with the statement that for all regular cardinals $\kappa \leq \lambda$, where $\kappa$ is the successor of a regular cardinal, there is a rigid saturated ideal on $\mathcal{P}_\kappa\lambda$. We also show the consistency of some instances of rigid saturated ideals on $\mathcal{P}_\kappa\lambda$ where $\kappa$ is the successor of a singular cardinal. 
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References

SHOWING 1-10 OF 22 REFERENCES
Prikry-Type Forcings
One of the central topics of set theory since Cantor has been the study of the power function κ→2 κ . The basic problem is to determine all the possible values of 2 κ for a cardinal κ. Paul Cohen…
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…
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…
Canonical structure in the universe of set theory: part two
Rigid ideals
An ideal I on a cardinal κ is called rigid if all automorphisms of P(κ)/I are trivial. An ideal is called μ-minimal if whenever G ⊆ P(κ)/I is generic and X ∈ P(μ)V[G]V, it follows that V [X] = V [G].…
Ideals and Generic Elementary Embeddings
This chapter covers the technique of generic elementary embeddings. These embeddings are closely analogous to conventional large cardinal embeddings, the difference being that they are definable in…
Making the supercompactness of κ indestructible under κ-directed closed forcing
A model is found in which there is a supercompact cardinal κ which remains supercompact in any κ-directed closed forcing extension.
Iterated Forcing and Elementary Embeddings
I give a survey of some forcing techniques which are useful in the study of large cardinals and elementary embeddings. The main theme is the problem of extending a (possibly generic) elementary…
A uniqueness theorem for iterations
  • P. Larson
  • Mathematics
    Journal of Symbolic Logic
  • 2002
Abstract If M is a countable transitive model of , then for every real x there is a unique shortest iteration j: M → N with x ∈ N, or none at all.
The Higher Infinite
...
...