Submission date: 8 January 2014.

Abstract:

For n\geq 3, define T_n to be the theory of the generic K_n-free graph, where K_n is the complete graph on n vertices. We prove a graph theoretic characterization of dividing in T_n, and use it to show that forking and dividing are the same for complete types. We then give an example of a forking and nondividing formula. Altogether, T_n provides a counterexample to a recent question of Chernikov and Kaplan.

Mathematics Subject Classification:

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Full text arXiv 1401.1570: pdf, ps.