Recent results on definability lattices of numerical structures

Definability is one of the central concepts of mathematical logic and is one of the important concepts of all mathematics. At the same time, it is still relatively little studied.
The report will discuss the latest results related to definability lattices (reduct lattices) for numerical structures, such as, for example, the addition of rational numbers.
It is remarkable that a number of these results were obtained by high-school students at the May 2022 Program in “Sirius”.