On rational limits of Shelah—Spencer graphs

Journal of Symbolic Logic 77 (2):580-592 (2012)
Abstract
Given a sequence {a n } in (0,1) converging to a rational, we examine the model theoretic properties of structures obtained as limits of Shelah-Spencer graphs G(m, m -αn ). We show that in most cases the model theory is either extremely well-behaved or extremely wild, and characterize when each occurs
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