Abstract:

In the present paper we study properties of $p$-preserving convex-to-right (left) formulas in weakly
o-minimal theories, where $p$ is a non-algebraic 1-type. It is proved that in the case of an existence of a $p$-preserving convex-to-right (left) formula that is not equivalence-generating, there exists a $p$-preserving convex-to-left (right) formula that is also not equivalence-generating; it was shown how it is built from the original formula.