3 citations · 3 across the 6 of their papers we have counts for
6 papers
On the o-minimal Hilbert's fifth problem
Mario J. Edmundo, Marcello Mamino, Luca Prelli +2
Let be an arbitrary o-minimal structure. Let be a definably compact definably connected abelian definable group of dimension . Here we compute the new the intr…
Interpretable groups are definable
Janak Ramakrishnan, Ya'acov Peterzil, Pantelis Eleftheriou
We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesi…
Definable linear orders definably embed into lexicographic orders in o-minimal structures
Janak Ramakrishnan
We completely characterize definable linear orders in o-minimal structures expanding groups. For example, let (P,<_p) be a linear order definable in the real field R. Then (P,<_p)…
Functions continuous on curves in o-minimal structures
Janak Ramakrishnan
We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal field such that, for any bounded definable function, the germ of the function on an initial s…
Maximal small extensions of o-minimal structures
Janak Ramakrishnan
A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is poss…
Uniform bounds on growth in o-minimal structures
Janak Ramakrishnan
We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity by a function definable without paramete…