Erik Walsberg

collaborators

4 papers

math.LO2026

Trace definability IV: higher arity notions

Erik Walsberg

Motivated by the "composition theorems" of Chernikov-Hempel and Abd Aldaim-Conant-Terry we introduce $k$ -trace definability between first order theories. Any theory which is $k$ -tr…

math.LO2026

Trace definability III: Infinite dimensional space over a model of $T$

Erik Walsberg

We show that for a number of theories $T^{*}$ of model-theoretic interest there is a simpler theory $T$ and $κ \geq ℵ_{0}$ such that $T^{*}$ is trace equivalent to the theory of $κ$ -d…

math.LO2026

Trace definability II: model-theoretic linearity

Erik Walsberg

We give examples of $NIP$ structures in which new algebraic structure appears in the Shelah completion. In particular we construct a weakly o-minimal structure $\mathscr{M…

math.LO2025

Trace definability I: preservation and characterizations

Erik Walsberg

We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properti…

Trace definability IV: higher arity notions

Trace definability III: Infinite dimensional space over a model of T

Trace definability II: model-theoretic linearity

Trace definability I: preservation and characterizations

Trace definability III: Infinite dimensional space over a model of $T$