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We present a relatively simple description of binary, definable subsets ofmodels of weakly quasi-o-minimal theories. In particular, we closely describedefinable linear orders and prove a weak version of the monotonicity theorem.We also prove that weak quasi-o-minimality of a theory with respect to onedefinable linear order implies weak quasi-o-minimality with respect to anyother such order.

Does weak quasi-o-minimality behave better than weak o-minimality?