# Rigid ideals

@article{Cody2016RigidI, title={Rigid ideals}, author={Brent Cody and Monroe Eskew}, journal={Israel Journal of Mathematics}, year={2016}, volume={224}, pages={343-366} }

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]. We prove that the existence of a rigid saturated μ-minimal ideal on μ+, where μ is a regular cardinal, is consistent relative to the existence of large cardinals. The existence of such an ideal implies that GCH fails. However, we show that the existence of a rigid saturated ideal on μ+, where μ is… Expand

#### 2 Citations

More rigid ideals

- Mathematics
- Israel Journal of Mathematics
- 2019

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,… Expand

Combinatorial Principles and some questions concerning L-like properties and DC$_{\kappa}$

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- 2019

We extend a result of Arthur Apter which answer a question of Matthew Foreman and Menachem Magidor related to mutually stationary sets. We also extend a result of Arthur Apter which answer a question… Expand

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