We explore the properties of 1-types over sets in weakly o-minimal theories. We introduce and analyze six essential classes of non-algebraic 1-types (isolated, quasirational, irrational, quasisolitary, solitary, and social), highlighting the ways in which these types capture key convexity behaviors and definability conditions. Building on parallels with classical o-minimal theories, we establish lemmas and propositions that illustrate how properties extend from the o-minimal to the weakly o-minimal context. In particular, we demonstrate that one-types in these theories can often be decomposed into finitely many convex subsets or cuts, thereby preserving important one-dimensional geometric intuitions.
Baizhanov et al. (Thu,) studied this question.
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