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A simpler axiomatization of the Shelah-Spencer almost sure theories

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Abstract

We give an explicit AE-axiomatization of the almost sure theories of sparse random graphs G(n, n −α) of Shelah-Spencer. In the process we give a method of constructing extensions of graphs whose ‘relative dimension’ is negative, but arbitrarily small. We describe the existentially closed and locally finite models of the theory and produce types of dimension zero. We offer a useful characterization of forking and generalize results about stability and the Dimensional Order Property (DOP) that were known for graphs to arbitrary relational languages.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Michael C. Laskowski

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  1. Michael C. Laskowski
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Correspondence to Michael C. Laskowski.

Additional information

Partially supported by NSF grant DMS-0300080. The author thanks John Baldwin for several useful conversations.

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Laskowski, M.C. A simpler axiomatization of the Shelah-Spencer almost sure theories. Isr. J. Math. 161, 157–186 (2007). https://doi.org/10.1007/s11856-007-0077-8

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  • DOI: https://doi.org/10.1007/s11856-007-0077-8

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