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 2019Show all

7 papers · 1 filter

math.LO2019★ 5 cited

Directed sets and topological spaces definable in o-minimal structures

Pablo Andujar Guerrero, Margaret E. M. Thomas, Erik Walsberg

We study directed sets definable in o-minimal structures, showing that in expansions of ordered fields these admit cofinal definable curves, as well as a suitable analogue in expan…

math.LO2019★ 3 cited

An NIP structure which does not interpret an infinite group but whose Shelah expansion interprets an infinite field

Erik Walsberg

We describe one.

math.LO2019

Externally definable quotients and NIP expansions of the real ordered additive group

Erik Walsberg

Let $R$ be an $NIP$ expansion of $(R, <, +)$ by closed subsets of $R^{n}$ and continuous functions $f : R^{m} \to R^{n}$ . Then $\math…

math.LO2019★ 4 cited

Dp and other minimalities

Pierre Simon, Erik Walsberg

A first order expansion of $(R, +, <)$ is dp-minimal if and only if it is o-minimal. We prove analogous results for algebraic closures of finite fields, $p$ -adic fields, ord…

math.LO2019★ 1 cited

Dp-minimal expansions of discrete ordered abelian groups

Erik Walsberg

If $Z$ is a dp-minimal expansion of a discrete ordered abelian group $(Z, <, +)$ and $Z$ does not admit a nontrivial definable convex subgroup then $Z$ …

math.LO2019

Coarse dimension and definable sets in expansions of the ordered real vector space

Erik Walsberg

Suppose $E \subseteq R$ is nowhere dense. If $(R, <, +, (x \mapsto λ x)_{λ \in R}, E)$ does not define every bounded Borel subset of every $R^{n}$ the…

cs.LO2019★ 2 cited

Continuous Regular Functions

Alexi Block Gorman, Philipp Hieronymi, Elliot Kaplan +5

Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function $f : [0, 1] \to [0, 1]$ is $r$ -regular if there is a Büchi automaton that accepts precisely the set of base $r…