Randomness and Semigenericity
نویسندگان
چکیده
Let L contain only the equality symbol and let L+ be an arbitrary finite symmetric relational language containing L. Suppose probabilities are defined on finite L+ structures with ‘edge probability”’ n−α. By Tα, the almost sure theory of random L+-structures we mean the collection of L+-sentences which have limit probability 1. Tα denotes the theory of the generic structures for Kα, (the collection of finite graphs G with δα(G) = |G| − α · | edges of G | hereditarily nonnegative.) 0.1 Theorem. T α, the almost sure theory of random L+-structures is the same as the theory Tα of the Kα-generic model. This theory is complete, stable, and nearly model complete. Moreover, it has the Mathematics Review Numbers: 03C10, 05C80, keywords: random graphs, 0− 1-laws, stability Partially supported by NSF grant 9308768 and a visit to Simon Fraser University This is paper 528. Both authors thank Rutgers University and the Binational Science Foundation for partial support of this research.
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