Date of Award
Summer 2008
Document Type
Thesis - Restricted
Degree Name
Master of Science (MS)
Department
Mathematics, Statistics and Computer Science
First Advisor
Lemmp, Steffen
Second Advisor
Pastion, Francis
Third Advisor
Ruitenburg, Wim
Abstract
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.
Recommended Citation
Fleischmann, Jonathan A., "Syntactic Preservation Theorems and an Intuitionistic Formula Hierarchy" (2008). Master's Theses (1922-2009) Access restricted to Marquette Campus. 2153.
https://epublications.marquette.edu/theses/2153