Alex Savatovsky

activity

20182021

most citedExpansions of real closed fields which introduce no new smooth functions

2 citations · 2 across the 5 of their papers we have counts for

collaborators

Showing 2020Show all

3 papers · 1 filter

math.LO2020

Connectedness in structures on the real numbers: o-minimality and undecidability

Alfred Dolich, Chris Miller, Alex Savatovsky +1

We initiate an investigation of structures on the set of real numbers having the property that path components of definable sets are definable. All o\nobreakdash-\hspace{0pt}minima…

math.LO2020

Structure theorem for i-minimal expansions of the real additive ordered group

Alex Savatovsky

We prove that for an o-minimal expansion of the real additive group $R$ and a set $P \subseteq R$ of dimension $0$ such that $⟨ R, P ⟩$ is sparse, h…

math.LO2020

On semibounded expansions of ordered groups

Pantelis E. Eleftheriou, Alex Savatovsky

We explore "semibounded" expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if $\mathcal R=\langle R, <, +, \…