First-order logical statements for o-minimality

[sharma65]

There are two equivalent definitions for o-minimality: a set-theoretic and model-theoretic one, both of which can be found on Wikipedia (https://en.wikipedia.org/wiki/O-minimal_theory). Try to write down what it means for a structure to be o-minimal in first-order logic, either as a code comment or just with pen and paper (or LaTeX if you prefer).

[sharma65]

Reference for o-minimality.

https://www.fields.utoronto.ca/programs/scientific/08-09/o-minimal/geometry/Starchenko2.pdf

Reference for definable sets. Page 33 of these notes.

https://faculty.math.illinois.edu/~vddries/main2.pdf