The sheaf construction and its applications

Abstract

This thesis deals with the theory of sheaves and its applications. Definitions and constructions of sheaves are given and used to represent algebraic structures, reduced products and limit reduced products of L-structures. The notion of forcing in sheaves is discussed and used with the representation theorems to derive Los' theorem. The notion of h-limit theories is given and used to prove that a theory is an h-limit theory iff it is invariant under global sections. Some other preservation theorems for first order sentences are proved. These results are applied to derive some model theoretical properties of some classes of rings.