PROPERTIES OF HYPERGRAPHS OF MODELS OF WEAKLY O-MINIMAL THEORIES

In this paper, we study the notions of relative H-freedom and H-independence for hypergraphs models weakly o-minimal theories. Hypergraphs a theory are derived objects that allow obtaining essential structural information both about theories themselves related semantic objects. Recall hypergraph is any pair sets (X, Y), where Y some subset Boolean P(X) set X. case, X called support elements from edges Y). Weak o-minimality was originally deeply investigated by D. Macpherson, Marker, C. Steinhorn. nineties last century, Kazakhstan scientists successfully joined concept, solving number problems posed authors. continue model-theoretic properties structures. A criterion realizations non-algebraic 1-type in almost omega-categorical obtained terms convexity rank. We also establish two 1-types weak orthogonality 1-types.