مشخصات پژوهش

. Let M = (M, <, +, ...) be a weakly o-minimal non-valuational structure expanding an ordered group. We show that the full first-order theory Th(M) has definable Skolem functions if and only if isolated types in SMn (A) are dense for each A ⊆ M and n ∈ N. Using this, we prove that no strictly weakly o-minimal non-valuational expansion of an ordered group has definable Skolem functions, thereby answering Conjecture 1.7 of Eleftheriou et al. (On definable Skolem functions in weakly o-minimal non-valuational structures. J. Symb. Logic, vol. 82 (2017), no. 4).