Forking and Dividing in Henson Graphs
نویسندگان
چکیده
منابع مشابه
Forking and Dividing in Henson Graphs
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 recent question of Chernikov and K...
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We investigate an open question concerning properties of algebraic independence in continuous theories (see Section 4). The rest of the work is essentially a translation to continuous logic of popular notions of independence (in particular, forking and dividing). Much of the time we are simply “copying” classical proofs from well-known sources, while along the way making the necessary adjustmen...
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We prove that in theories without the tree property of the second kind (which include dependent and simple theories) forking and dividing over models are the same, and in fact over any extension base. As an application we show that dependence is equivalent to bounded forking assuming NTP2.
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variety). For each i, let φi(x) be a C-dense quantifier-free Li-formula with parameters from K. Then we can find a K-definable rational function f : C → P which is non-constant, and has the property that the divisor f−1(0) is a sum of distinct points in ⋂n i=1 φi(K), with no multipliticities. (In particular, the support of the divisor contains no points from C(K)\C(K) and no points from C \ C.)...
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We discuss groups acting regularly on the Henson graphs Γn, answering a question posed by Peter Cameron, and we explore a number of related questions.
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2017
ISSN: 0029-4527
DOI: 10.1215/00294527-2017-0016