Itay Kaplan

collaborators

2 papers

math.LO2025

Cofinal families of finite VC-dimension

Omer Ben-Neria, Itay Kaplan, George Peterzil

Given infinite cardinals $θ \leq κ$ , we ask for the minimal VC-dimension of a cofinal family $F \subseteq [κ]^{< θ}$ . We show that for $θ = ω$ and $κ = ℵ_{n}$ it is consistent…

math.LO2024

Stable reducts of elementary extensions of Presburger arithmetic

Eran Alouf, Antongiulio Fornasiero, Itay Kaplan

Suppose $N$ is elementarily equivalent to an archimedean ordered abelian group $(G, +, <)$ with small quotients (for all $1 \leq n < ω$ , $[G : n G]$ is finite). Then every stable reduc…