Date of Award

Summer 2008

Degree 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.

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