Syntactic Preservation Theorems and an Intuitionistic Formula Hierarchy
Jonathan Fleischmann · e-Publications@Marquette (Marquette University) · 2008
We prove several syntactic preservation theorems for intuitionistic predicate logic. The first is an intuitionistic analogue of the generalized (dual of the) Lyndon-Los-Tarski Theorem, which characterizes the sentences preserved under inverse images of homomorphisms of Kripke models having certain reflection properties. The second is an intuitionistic analogue of the generalized Los-Tarski Theorem, which characterizes the sentences preserved under submodels having certain reflection properties. The third is a generalized Sandwich Theorem. We define several intuitionistic formula hierarchies analogous to the classical formula hierarchies \In (= II~) and 3n (= E~), and we obtain intuitionistic analogues of .the Keisler Sandwich Theorem for \In-sentences. Each of these theorems implies the corresponding classical theorem in the case where the Kripke models force classical logic.