arXiv subjects

Omer Ben-Neria

Publications and source records attributed to Omer Ben-Neria.

24 records · Page 2Linked to original sources

arXiv2017

On 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 \cite{ForMag-MS}. We obtain two consistency results which show that it is possible for a sequence of regular cardinals $( κ_n )_{n < ω}$ to have the property that for every sequence $\vec{S}$, of some fixed-cofinality stationary sets $S_n \subseteq κ_n$, $\vec{S}$ is tightly stationary in a generic extension. The results are obtained using variations of the short-extenders forcing method.

math.LO↗

arXiv2017

On 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 concerning stationary sequences on the first uncountable cardinals, $\aleph_n$, $1 \leq n < ω$.

math.LO↗

arXiv2017

Diamonds, Compactness, and Measure Sequences

We establish the consistency of the failure of the diamond principle on a cardinal $κ$ which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of $κ$ in a Radin generic extension.

math.LO↗

arXiv2015

On the Splitting Number at Regular Cardinals

Let $κ$,$λ$ be regular uncountable cardinals such that $λ> κ^+$ is not a successor of a singular cardinal of low cofinality. We construct a generic extension with $s(κ) = λ$ starting from a ground model in which $o(κ) = λ$ and prove that assuming $\neg 0^¶$, $s(κ) = λ$ implies that $o(κ) \geq λ$ in the core model.

math.LO↗

arXiv2015

The structure of the Mitchell order - I

We isolate here a wide class of well founded orders called tame orders and show that each such order of cardinality at most $κ$ can be realized as the Mitchell order on a measurable cardinal $κ$, from a consistency assumption weaker than $o(κ) = κ^+$.

math.LO↗

arXiv2015

The structure of the Mitchell order - II

We address the question regarding the structure of the Mitchell order on normal measures. We show that every well founded order can be realized as the Mitchell order on a measurable cardinal $κ$ from some large cardinal assumption.

math.LO↗