Eran Alouf

activity

20172024

collaborators

4 papers

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…

math.LO2024

On dp-minimal expansions of the integers II

Eran Alouf

We first prove that if $Z$ is a dp-minimal expansion of $(Z, +, 0, 1)$ which is not interdefinable with $(Z, +, 0, 1, <)$ , then every inf…

math.LO2020

On dp-minimal expansions of the integers

Eran Alouf

We show that if $Z$ is a dp-minimal expansion of $(Z, +, 0, 1)$ that defines an infinite subset of $N$ , then $Z$ is interdefin…

math.LO2017

A new dp-minimal expansion of the integers

Eran Alouf, Christian d'Elbée

We consider the structure $(Z, +, 0, ∣_{p_{1}}, \dots, ∣_{p_{n}})$ , where $x ∣_{p} y$ means $v_{p} (x) \leq v_{p} (y)$ and $v_{p}$ is the $p$ -adic valuation. We prove that its theory…