Table of Contents

Syntactic Considerations.- Modal Structures and Morphisms.- Validity.- Completeness.- Löwenheim-Skolem Theorems.- Ultraproducts.- Ultrafilter Pairs and Elementary Embeddings.- Direct Limits.- Model Extensions.- Inductive Theories.- Joint Consistency and Interpolation.- Model Completeness.- Finite Forcing.- Forcing and Model Completions.- Omitting Types and a Two-Cardinal Theorem.