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arXiv · 1401.1570

Forking and dividing in Henson graphs

Gabriel Conant
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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.

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Gabriel Conant. 2014-01-08. Forking and dividing in Henson graphs. https://doi.org/10.1215/00294527-2017-0016

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