7 papers
Rudin-Keisler capturing and Mutual Stationairy at successors of Singulars
Dominik Adolf, Omer Ben-Neria
We introduce a combinatorial notion of measures called Rudin-Keisler capturing and use it to give a new construction of elementary substructures around singular cardinals. The new…
Projective Determinacy from long Chang's Conjecture
Dominik Adolf
Consider the property . Here we will show that this property with the addition of the General Co…
Ideals and Strong Axioms of Determinacy
Dominik Adolf, Grigor Sargsyan, Nam Trang +2
We show that the following two theories are equiconsistent: (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal such that if j is the generic embedding associ…
Approachable Free Subsets and Fine Structure Derived Scales
Dominik Adolf, Omer Ben-Neria
Shelah showed that the existence of free subsets over internally approachable subalgebras follows from the failure of the PCF conjecture on intervals of regular cardinals. We show…
Some basic thoughts on the cofiality of Chang structures with an application to forcing
Dominik Adolf
Consider where is an uncountable regular cardinal. By a result of Shelah's we have for alm…
Lower consistency bounds for mutual stationarity with divergent cofinalities and limited covering
Dominik Adolf
We improve previous work on the consistency strength of mutually stationary sequences of sets concentrating on points with divergent cofinality building on previous work by Adolf,…
Lower consistency bounds for mutual stationarity with divergent uncountable cofinalities
Dominik Adolf, Sean Cox, Philip Welch
We prove that the upper bounds for the consistency strength of certain instances of mutual stationarity considered by Liu-Shelah~\cite{MR1469093} are close to optimal. We also cons…