Dependent first order theories, continued

By Saharon Shelah. 2004

136 citations recorded by the source corpus.

A dependent theory is a (first order complete theory) T which does not have the independence property. A major result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being dependent. Another one justifies the cofinality restriction in the theorem (from a previous work) saying that pairwise perpendicular indiscernible sequences, can have arbitrary dual-cofinalities in some models containing them. We introduce “strongly dependent” and look at definable groups; and also at dividing, forking and relatives.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/707d690d553827a8110bea196a44ced46ebb1839

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

On NIP and invariant measures (2007, background): “A final question is whether given a definable group G in a NIP theory T , there are some reasonable assumptions which imply that G/G00 is semi-ominimal (in the Shelah expansion) or at least o-minimally analysable.”
Introduction to theories without the independence property (2008, background): “stable and strongly dependent), to just being stable [ 47 , 49].”
Additivity of the dp-rank (2011, background): “In particular, can one characterize theories with finite dp-rank (which Shelah calls strongly dependent theories in [4]) in terms of VC-density? If we know that every type p(x) in models of a theory T have dp-rank n, does this say anything about the VC-density of the types? We address some of this q”