Omitting Types in Fragments and Extensions of First Order Logic

Abstract

Fix \(2 < n < \omega\). 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 \(L_{\omega, \omega}\).

Keywords

• algebraic logic
• multimodal logic
• omitting types
• completions