# Sh:783

• Shelah, S. (2009). Dependent first order theories, continued. Israel J. Math., 173, 1–60.
• Abstract:
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.
• Version 2015-03-04_10 (65p) published version (60p)
Bib entry
@article{Sh:783,
author = {Shelah, Saharon},
title = {{Dependent first order theories, continued}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {173},
year = {2009},
pages = {1--60},
issn = {0021-2172},
mrnumber = {2570659},
mrclass = {03C45 (03C64)},
doi = {10.1007/s11856-009-0082-1},
note = {\href{https://arxiv.org/abs/math/0406440}{arXiv: math/0406440}},
arxiv_number = {math/0406440}
}