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Randomness and semigenericity
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^{- alpha}. By T^alpha, the
almost sure theory of random L^+-structures we mean the collection of
L^+-sentences which have limit probability 1. T_alpha denotes the theory of the
generic structures for K_alpha, (the collection of finite graphs G with
delta_{alpha}(G)=|G|- alpha. | edges of G | hereditarily nonnegative.)
THEOREM: T_alpha, the almost sure theory of random L^+-structures is the same
as the theory T_alpha of the K_alpha-generic model. This theory is complete,
stable, and nearly model complete. Moreover, it has the finite model property
and has only infinite models so is not finitely axiomatizable
Reimarus and the Return of Christ Revisited: Reflections on Luke 21:24b and Its Phrase Times of the Gentiles in Historicist Perspective
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