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We work throughout in a finite relational language L. This paper is built on  and . 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  is needed to read this paper. Spencer and Shelah  constructed for each irrational α between 0 and 1 the theory T α as the almost sure theory of random graphs with edge probability n −α. In  we proved that this was the same theory as thedoi:10.2307/2586841 fatcat:6rahqu2uijfsrj6z4v4mgwt4uq