arXiv subjects

Esther Elbaz Saban

Publications and source records attributed to Esther Elbaz Saban.

2 recordsLinked to original sources

arXiv2026

O-minimal open core is not an elementary property

Given a structure $\mathcal{M}$ with a definable topology, its open core is a structure defined on the same universe whose language consists of all open sets of all arities definable in $\mathcal{M}$. In response to questions raised by Dolich, Miller, and Steinhorn in their early work on open core, we prove that having an o-minimal open core is not an elementary property. In particular, we construct an expansion of the structure $(\mathbb{Q},<)$ that has an o-minimal open core, but some of its elementary superstructures do not.

math.LO↗

arXiv2020

Grothendieck ring of the pairing function without cycles

A bijection $(l,r)$ between $M^2$ and $M$ is said to be a pairing function with no cycles, if any composition of its coordinate functions has no fixed point. We compute here the Grothendieck ring of the pairing function without cycles to be isomorphic to $\mathbb{Z}^2\simeq \mathbb{Z}[X]/(X-X^2)$. More generally, for any $n\in \mathbb{N}^*$ and any bijetion without cycles betwen $M$ and $M^n$, the exact same method proves that $K_0(M)=\mathbb{Z}[X]/(X-X^n)$.

math.LO↗