Forking and Dividing in Henson Graphs
نویسنده
چکیده
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 Kaplan.
منابع مشابه
Forking and dividing in NTP₂ theories
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.
متن کاملThorn-forking as Local Forking
We introduce the notion of a preindependence relation between subsets of the big model of a complete first-order theory, an abstraction of the properties which numerous concrete notions such as forking, dividing, thorn-forking, thorn-dividing, splitting or finite satisfiability share in all complete theories. We examine the relation between four additional axioms (extension, local character, fu...
متن کاملAn Independence Theorem for Ntp2 Theories
We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as array-dividing. Combining it with existence of strictly invariant sequences we deduce that forking satisfies the chain condition over extension bases (namely, the forking ideal is S1, in Hrushovski’s terminology). Using it we prove an independence theorem over extension bases (whic...
متن کاملForking and Dividing in Continuous Logic
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...
متن کاملHenson Graphs and Urysohn-henson Graphs as Cayley Graphs Dedicated to Professor Anatoly Vershik on the Occasion of His 80th Birthday
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Notre Dame Journal of Formal Logic
دوره 58 شماره
صفحات -
تاریخ انتشار 2017