This topics course may follow one of the following paths through model theory: application of the theory of Boolean algebras--e.g., Stone's topological duality--to logic, including the compactness theorem, the omitting types theorem, the classification of aleph-zero-categorical theories, and the independence of the continuum hypothesis; the theory of existentially closed structures and what they look like among fields, ordered fields, p-valued fields, and lattice-ordered Abelian groups. |