{"DOI":"10.2307/2586841","abstract":"We work throughout in a finite relational language L. This paper is built on [2] and [3]. We repeat some of the basic notions and results from these papers for the convenience of the reader but familiarity with the setup in the first few sections of [3] is needed to read this paper. Spencer and Shelah [6] constructed for each irrational \u03b1 between 0 and 1 the theory T\n \u03b1 as the almost sure theory of random graphs with edge probability n\n \u2212\u03b1. In [2] we proved that this was the same theory as the theory T\n \u03b1 built by constructing a generic model in [3]. In this paper we explore some of the more subtle model theoretic properties of this theory. We show that T\n \u03b1 has the dimensional order property and does not have the finite cover property.\n We work in the framework of [3] so probability theory is not needed in this paper. This choice allows us to consider a wider class of theories than just the T\n \u03b1. The basic facts cited from [3] were due to Hrushovski [4]; a full bibliography is in [3]. For general background in stability theory see [1] or [5].\n We work at three levels of generality. The first is given by an axiomatic framework in Context 1.10. Section 2 is carried out in this generality. The main family of examples for this context is described in Example 1.3. Sections 3 and 4 depend on a function \u03b4 assigning a real number to each finite L-structure as in these examples. Some of the constructions in Section 3 (labeled at the time) use heavily the restriction of the class of examples to graphs. The first author acknowledges useful discussions on this paper with Sergei Starchenko.","author":[{"family":"Baldwin"},{"family":"Shelah"}],"id":"unknown","issue":"02","issued":{"date-parts":[[1998]]},"language":"en","page-first":"427","publisher":"Cambridge University Press (CUP)","title":"DOP and FCP in generic structures","type":"article-journal","volume":"63"}