Itay Kaplan

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math.LO2025

Cofinal families of finite VC-dimension

Omer Ben-Neria, Itay Kaplan, George Peterzil

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

math.LO2025

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 < I ¨ $ , $[G : n G]$ is finite). Then every stable redu…