Omitting Types in Fragments and Extensions of First Order Logic - Sayed Ahmed, Tarek (Bulletin of the Section of Logic, 2021)
Fix \(2 < n < ω\). Let \(L_n\) denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \(L_n\) and for infinitary variants and extensions of \(L_ω, ω\).