2 citations · 2 across the 5 of their papers we have counts for
5 papers
Defining new linear functions in tame expansions of the real ordered additive group
Alex Savatovsky
We explore \emph{semibounded} expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We introduce the notion of a \emph{semibo…
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…
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 and a set of dimension such that is sparse, h…
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, <, +, \…
Expansions of real closed fields which introduce no new smooth functions
Pantelis E. Eleftheriou, Alex Savatovsky
We prove the following theorem: let be an expansion of the real field , such that every definable set (I) is a uniform countable unio…