The Ben-david Magidor Model
نویسنده
چکیده
In [2], it was shown that it is consistent that there is a singular cardinal μ such that μ carries a uniform, λ indecomposable filter for every λ ∈ (cf(μ), μ) ∩REG. This was done using the forcing from [8]. In this note, we present an expanded version of the proof using the forcing from [8] without interleaved collapses. I had independent reasons for wanting to go through this material, and I figured making this material available might benefit someone. In particular, I was interested in the consistency of the the failure of SCH at μ while there exists an ideal I in μ which is λ indecomposable for all λ ∈ cf(μ), μ)∩REG, א1-weakly saturated, and extends the non-stationary ideal. The consistency of such things is related to the question of whether or not there can be a successor of singular which is Jónsson.
منابع مشابه
On Box, Weak Box and Strong Compactness
One of the most important goals of set theorists over the last few years has been to re-prove old results which previously had used very strong assumptions from hypotheses which, at least prima facie, are weaker. Examples of these abound, including, but certainly not limited to, the work of Woodin and Cummings (see [3]) on the Singular Cardinals Problem, in which results previously obtained by ...
متن کاملOn Sequences Generic in the Sense of Magidor
The main result of this paper is a combinatorial characterization of Magidor-generic sequences. Using this characterization, I show that the critical sequences of certain iterations are Magidor-generic over the target model. I then employ these results in order to analyze which other Magidor sequences exist in a Magidor extension. One result in this direction is that if we temporarily identify ...
متن کاملOn Singular Stationarity I (Mutual Stationarity and Ideal-Based methods)
We study several ideal-based constructions in the context of singular stationarity. By combining methods of strong ideals, supercompact embeddings, and Prikry-type posets, we obtain three consistency results concerning mutually stationary sets, and answer a question of Foreman and Magidor ([7]) concerning stationary sequences on the first uncountable cardinals, אn, 1 ≤ n < ω.
متن کاملOn Singular Stationarity II (tight stationarity and extenders-based methods)
We study the notion of tightly stationary sets which was introduced by Foreman and Magidor in [8]. We obtain two consistency results which show that it is possible for a sequence of regular cardinals hnin<! to have the property that for every sequence ~ S, of some fixed-cofinality stationary sets Sn ✓ n, ~ S is tightly stationary in a generic extension. The results are obtained using variatio...
متن کامل