# Sh:886

- Shelah, S. (2017).
*Definable groups for dependent and 2-dependent theories*. Sarajevo J. Math.,**13(25)**(1), 3–25. arXiv: math/0703045 DOI: 10.5644/SJM.13.1.01 MR: 3666349 -
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} }