Forking and Dividing in Henson Graphs

Notre Dame Journal of Formal Logic 58 (4):555-566 (2017)
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Abstract

For n≥3, define Tn to be the theory of the generic Kn-free graph, where Kn is the complete graph on n vertices. We prove a graph-theoretic characterization of dividing in Tn 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, Tn provides a counterexample to a question of Chernikov and Kaplan.

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10.1215/00294527-2017-0016

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Citations of this work

Generic expansion and Skolemization in NSOP 1 theories.Alex Kruckman & Nicholas Ramsey - 2018 - Annals of Pure and Applied Logic 169 (8):755-774.
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Three Surprising Instances of Dividing.Gabriel Conant & Alex Kruckman - forthcoming - Journal of Symbolic Logic:1-20.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
A geometric introduction to forking and thorn-forking.Hans Adler - 2009 - Journal of Mathematical Logic 9 (1):1-20.
Forking and dividing in NTP₂ theories.Artem Chernikov & Itay Kaplan - 2012 - Journal of Symbolic Logic 77 (1):1-20.
Toward classifying unstable theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.

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