Itay Kaplan

activity

20062026

most citedThe Borel cardinality of Lascar strong types

10 citations · 41 across the 29 of their papers we have counts for

collaborators

45 papers

math.GR2026

An automorphism tower of length $κ^{+}$

Yatir Halevi, Itay Kaplan

For any infinite cardinal $κ$ , we give an example of a centerless group $G$ of cardinality $κ$ whose automorphism tower terminates after $κ^{+}$ steps, answering a question of Simon…

math.LO2024

Infinite Cliques in Simple and Stable Graphs

Yatir Halevi, Itay Kaplan, Saharon Shelah

Suppose that $G$ is a graph of cardinality $μ^{+}$ with chromatic number $χ (G) \geq μ^{+}$ . One possible reason that this could happen is if $G$ contains a clique of size $μ^{+}$ . We prov…

math.LO2023

Generic Stability Independence and Treeless theories

Itay Kaplan, Nicholas Ramsey, Pierre Simon

We initiate a systematic study of \emph{generic stability independence} and introduce the class of \emph{treeless theories} in which this notion of independence is particularly wel…

math.LO2023

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…

math.LO2022

A definable $(p, q)$ -theorem for NIP theories

Itay Kaplan

We prove a definable version of Matoušek's $(p, q)$ -theorem in NIP theories. This answers a question of Chernikov and Simon. We also prove a uniform version. The proof builds on a p…

math.LO2022★ 1 cited

On large externally definable sets in NIP

Martin Bays, Omer Ben-Neria, Itay Kaplan +1

We study cofinal systems of finite subsets of $ω_{1}$ . 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…

An automorphism tower of length κ+