On the Model Theory of Random Graphs

Abstract

Hrushovski's amalgamation construction can be used to join a

collection of finite graphs to produce a ``generic'' of this

collection. The choice of the collection and the way they are joined

are determined by a real-valued parameter α. Classical results

have shown that for α irrational in (0,1), the model theory

of the resulting structure is very well-behaved.

This dissertation examines analogous constructions for rational <italic>r</italic>.

Depending on the way in which the parameter's control of the

construction is defined, the model theory of the resulting generic

will be either very well-behaved or very wild. We characterize when

each of these situations occurs.