7 citations · 9 across the 18 of their papers we have counts for
24 papers
Cofinal families of finite VC-dimension
Omer Ben-Neria, Itay Kaplan, George Peterzil
Given infinite cardinals , we ask for the minimal VC-dimension of a cofinal family . We show that for and it is consistent…
Jonsson and Magidor filters
Omer Ben-Neria, Shimon Garti
We study the filter versions of square bracket partition relations, focusing on Jonssonicity and Magidority. We show that the singular cardinals in a Kleinberg sequence above some…
A Kunen-Like Model with a Critical Failure of the Continuum Hypothesis
Omer Ben-Neria, Eyal Kaplan
We construct a model of the form that exhibits the simplest structural behavior of -complete ultrafilters in a model of set theory with a single measurable cardinal …
Aronszajn trees and maximality
Omer Ben-Neria, Siiri Kivimäki, Menachem Magidor +1
Assuming the consistency of a weakly compact cardinal above a regular uncountable cardinal , we prove the consistency of the existence of a wide -Aronszajn tree, i.e. a tre…
The model theory of geometric random graphs
Omer Ben-Neria, Itay Kaplan, Tingxiang Zou
We study the logical properties of infinite geometric random graphs, introduced by Bonato and Janssen. These are graphs whose vertex set is a dense ``generic'' subset of a metric s…
On -Definable Closed Unbounded Sets
Omer Ben-Neria, Philipp Lücke
Definable stationary sets, and specifically, ordinal definable ones, play a significant role in the study of canonical inner models of set theory and the class HOD of hereditarily…
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…
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…
On large externally definable sets in NIP
Martin Bays, Omer Ben-Neria, Itay Kaplan +1
We study cofinal systems of finite subsets of . We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a questi…
Compactness and Guessing Principles in the Radin Extensions
Omer Ben-Neria, Jing Zhang
We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension wi…
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…
Club Stationary Reflection and the Special Aronszajn Tree Property
Omer Ben-Neria, Thomas Gilton
We prove that it is consistent that Club Stationary Reflection and the Special Aronszajn Tree Property simultaneously hold on , thereby contributing to the study of the tensio…
On -Strongly Measurable Cardinals
Omer Ben-Neria, Yair Hayut
We prove several consistency results concerning the notion of -strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hy…
Stationary Reflection and the failure of SCH
Omer Ben-Neria, Yair Hayut, Spencer Unger
In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and eve…
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…
Diamonds, Compactness, and Measure Sequences
Omer Ben-Neria
We establish the consistency of the failure of the diamond principle on a cardinal which satisfies a strong simultaneous reflection property. The result is based on an analysis…
Weak prediction principles
Omer Ben-Neria, Shimon Garti, Yair Hayut
We prove the consistency of the failure of the weak diamond at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond is equivalent to t…
Diagonal supercompact Radin forcing
Omer Ben-Neria, Chris Lambie-Hanson, Spencer Unger
Motivated by the goal of constructing a model in which there are no -Aronszajn trees for any regular , we produce a model with many singular cardinals where both the…
The structure of the Mitchell order - II
Omer Ben-Neria
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 measurabl…
The structure of the Mitchell order - I
Omer Ben-Neria
We isolate here a wide class of well founded orders called tame orders and show that each such order of cardinality at most can be realized as the Mitchell order on a measurabl…
On the Splitting Number at Regular Cardinals
Omer Ben-Neria, Moti Gitik
Let , be regular uncountable cardinals such that is not a successor of a singular cardinal of low cofinality. We construct a generic extension with starti…