## 2 Citations

### Another method for constructing models of not approachability and not SCH

- MathematicsArch. Math. Log.
- 2021

A new method of constructing a model of SCH+ is presented, which simplifies the construction of models of the model of AP by 90% and halves the complexity of the original model by 90%.

### Global Chang’s Conjecture and singular cardinals

- Materials ScienceEuropean journal of mathematics
- 2021

It is proved relative to large cardinals that Chang’s Conjecture can consistently hold between all pairs of limit cardinals below the minimal level.

## References

SHOWING 1-10 OF 44 REFERENCES

### The tree property at successors of singular cardinals

- MathematicsArch. Math. Log.
- 1996

It is shown that if $\ lambda$ is a singular limit of strongly compact cardinals, then $\lambda^+$ carries no Aronszajn trees.

### The Tree Property

- Mathematics, Economics
- 1998

Abstract We construct a model in which there are no ℵn-Aronszajn trees for any finiten⩾2, starting from a model with infinitely many supercompact cardinals. We also construct a model in which there…

### Successive failures of approachability

- Mathematics
- 2017

Motivated by showing that in ZFC we cannot construct a special Aronszajn tree on some cardinal greater than $\aleph_1$, we produce a model in which the approachability property fails (hence there are…

### Making the supercompactness of κ indestructible under κ-directed closed forcing

- Mathematics
- 1978

A model is found in which there is a supercompact cardinal κ which remains supercompact in any κ-directed closed forcing extension.

### The tree property and the failure of SCH at uncountable cofinality

- MathematicsArch. Math. Log.
- 2012

Given a regular cardinal λ and λ many supercompact cardinals, we describe a type of forcing such that in the generic extension there is a cardinal κ with cofinality λ, the Singular Cardinal…

### The tree property and the failure of the Singular Cardinal Hypothesis at ℵω2

- MathematicsThe Journal of Symbolic Logic
- 2012

Abstract We show that given ω many supercompact cardinals, there is a generic extension in which the tree property holds at ℵω2+ 1 and the SCH fails at ℵω2.

### Prikry-Type Forcings

- Mathematics
- 2010

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…

### A model for a very good scale and a bad scale

- MathematicsJournal of Symbolic Logic
- 2008

A type of forcing is described such that in the generic extension the cofinality of κ is λ, there is a very good scale at κ, a bad scale atκ, and SCH at λ fails.