7 papers
Approximating diamond principles on products at an inaccessible cardinal
Omer Ben-Neria, Jing Zhang
We isolate \emph{the approximating diamond principles}, which are consequences of the diamond principle at an inaccessible cardinal. We use these principles to find new methods for…
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…
Infinite decreasing chains in the Mitchell order
Omer Ben-Neria, Sandra Müller
It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order…
On configurations concerning cardinal characteristics at regular cardinals
Omer Ben-Neria, Shimon Garti
We study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak{s}_θ,\mathfrak{p}_θ,\mathfrak{g}_θ,\mathfrak{r}_θ,\ma…
On Singular Stationarity II (tight stationarity and extenders-based methods)
Omer Ben-Neria
We study the notion of tightly stationary sets which was introduced by Foreman and Magidor in \cite{ForMag-MS}. We obtain two consistency results which show that it is possible for…
On Singular Stationarity I (mutual stationarity and ideal-based methods)
Omer Ben-Neria
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 obtai…