Fundamentals of forking
نویسندگان
چکیده
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 کاملA Geometric Introduction to Forking and Thorn-forking
A ternary relation |̂ between subsets of the big model of a complete first-order theory T is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence relations as mathematical objects worth study...
متن کاملLecture Notes on Forking
1.1. Types. Most of the time we fix a complete countable first-order theory T in a language L, and we let M be a very saturated model of it, a “monster” model. All our sets and models are subsets and elementary submodels of M. A set is called small if it is cardinality is smaller than the saturation of M. For a set A, we let Def (A) be the boolean algebra of A-definable subsets of M, i.e. sets ...
متن کاملForking in VC-minimal theories
We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M , generalizing a result of Dolich on o-minimal theories in [4].
متن کاملAround stable forking
In the past few years various conjectures have been made concerning the relationship between simple theories and stable theories. The general thrust is that in a simple theory T forking should be accounted for by some kind of “stable fragment” of T . These issues were raised in discussions between Hart, Kim and Pillay in the Fields Institute in the autumn of 1996, but it is quite likely that ot...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1984
ISSN: 0168-0072
DOI: 10.1016/0168-0072(84)90005-8