Forking and dividing in NTP₂ theories
نویسندگان
چکیده
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.
منابع مشابه
Thorn-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 کاملLascar strong types and forking in NIP theories
This is an updated and slightly expanded version of a tutorial given in the Mini-Course in Model Theory, Torino, February 9-11, 2011. Some parts were previously exposed in the Model Theory Seminar of Barcelona. The main goals were to clarify the relation of forking with some versions of splitting in NIP theories and to present the known results on G-compactness, including a full proof of a theo...
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 کاملQualifying Exam Syllabus
Basic constructions: The completeness and compactness theorems. The Löwenheim-Skolem theorem. Omitting types. Ultraproducts. Indiscernible sequences. Nice properties: Saturation, homogeneity, and the monster model. Elimination of imaginaries and Meq. Quantifier elimination. Model completeness. Countably categorical theories. Stable theories: Characterizations of a stable formula. Stable, supers...
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:
- J. Symb. Log.
دوره 77 شماره
صفحات -
تاریخ انتشار 2012