Some time ago this question was asked: mathoverflow.net/questions/352344 . Is the formula from the accepted answer A=∅ really a positive formula? I don't have access to the linked article, but in another article i read positive set theory is formulated in a language (∈, =). So the formula from the answer (A=∅) would need to be expanded to something along the lines of ∀y.y∉A which is not positive.