# Sh:886

• Shelah, S. (2017). Definable groups for dependent and 2-dependent theories. Sarajevo J. Math., 13(25)(1), 3–25.
• Abstract:
Let T be a (first order complete) dependent theory, {\mathfrak{C}} a \bar{\kappa}-saturated model of T and G a definable subgroup which is abelian. Among subgroups of bounded index which are the union of <\kappa type definable subsets there is a minimal one, i.e. their intersection has bounded index. In fact, the bound is \leq 2^{|T|}. We then deal with 2-dependent theories, a wider class of first order theories.
• Version 2017-06-09_12 (19p) published version (23p)
Bib entry
@article{Sh:886,
author = {Shelah, Saharon},
title = {{Definable groups for dependent and 2-dependent theories}},
journal = {Sarajevo J. Math.},
fjournal = {Sarajevo Journal of Mathematics},
volume = {13(25)},
number = {1},
year = {2017},
pages = {3--25},
issn = {1840-0655},
mrnumber = {3666349},
mrclass = {03C45 (03C60)},
doi = {10.5644/SJM.13.1.01},
note = {\href{https://arxiv.org/abs/math/0703045}{arXiv: math/0703045}},
arxiv_number = {math/0703045}
}