Erik Walsberg

activity

20132026

most citedTame Topology over Dp-minimal Structures

12 citations · 63 across the 29 of their papers we have counts for

collaborators

Showing 2020Show all

6 papers · 1 filter

math.LO2020★ 2 cited

Galois groups of large fields with simple theory (with an appendix by Philip Dittmann)

Anand Pillay, Erik Walsberg

Suppose that $K$ is an infinite field which is large (in the sense of Pop) and whose first order theory is simple. We show that $K$ is {\em bounded}, namely has only finitely many…

math.LO2020★ 7 cited

The étale-open topology and the stable fields conjecture

Will Johnson, Chieu-Minh Tran, Erik Walsberg +1

For an arbitrary field $K$ and $K$ -variety $V$ , we introduce the étale-open topology on the set $V (K)$ of $K$ -points of $V$ . This topology agrees with the Zariski topology, Euclide…

math.LO2020

A P-adic structure which does not interpret an infinite field but whose Shelah completion does

Erik Walsberg

We give a $p$ -adic example of a structure whose Shelah completion interprets $Q_{p}$ but which does not (provided an extremely plausible conjecture holds) interpret an infin…

math.LO2020

Nippy proofs of p-adic results of Delon and Yao

Erik Walsberg

Let $K$ be an elementary extension of $Q_{p}$ , $V$ be the set of finite $a \in K$ , $st$ be the standard part map $K^{m} \to Q_{p}^{m}$ , and $X \subseteq K^{m}$ be…

math.LO2020★ 1 cited

Dp-minimal expansions of $(Z, +)$ via dense pairs via Mordell-Lang

Erik Walsberg

This is a contribution to the classification problem for dp-minimal expansions of $(Z, +)$ . Let $S$ be a dense cyclic group order on $(Z, +)$ . We use results on "de…

math.LO2020★ 2 cited

Generalizing a theorem of Bès and Choffrut

Erik Walsberg

Bès and Choffrut recently showed that there are no intermediate structures between $(R, <, +)$ and $(R, <, +, Z)$ . We prove a generalization: if $R$ …

Galois groups of large fields with simple theory (with an appendix by Philip Dittmann)

The étale-open topology and the stable fields conjecture

A P-adic structure which does not interpret an infinite field but whose Shelah completion does

Nippy proofs of p-adic results of Delon and Yao

Dp-minimal expansions of (Z,+) via dense pairs via Mordell-Lang

Generalizing a theorem of Bès and Choffrut

Dp-minimal expansions of $(Z, +)$ via dense pairs via Mordell-Lang