Israel Journal of Mathematics

, 173:1

Dependent first order theories, continued


DOI: 10.1007/s11856-009-0082-1

Cite this article as:
Shelah, S. Isr. J. Math. (2009) 173: 1. doi:10.1007/s11856-009-0082-1


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.

Copyright information

© Hebrew University Magnes Press 2009

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of Mathematics, Hill Center-Busch Campus RutgersThe State University of New JerseyPiscatawayUSA