DOP and FCP in generic structures

Abstract

Spencer and Shelah [ShSp:304] constructed for each irrational alpha between 0 and 1 the theory T^alpha as the almost sure theory of random graphs with edge probability n^{- alpha}. In [BlSh:528] we proved that this was the same theory as the theory T_alpha built by constructing a generic model in Baldwin and Shi. In this paper we explore some of the more subtle model theoretic properties of this theory. We show that T^alpha has the dimensional order property and does not have the finite cover property.