%0 Journal Article %1 shelah2007definable %A Shelah, Saharon %D 2007 %K model theory %T Definable groups for dependent and 2-dependent theories %U http://arxiv.org/abs/math/0703045 %X Let T be a (first order complete) dependent theory, C a 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 <= 2^|T| . We then deal with 2-dependent theories, a wider class of first order theories.

@article{shelah2007definable, abstract = {Let T be a (first order complete) dependent theory, C a 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 <= 2^{|T|} . We then deal with 2-dependent theories, a wider class of first order theories.}, added-at = {2014-11-20T01:44:56.000+0100}, author = {Shelah, Saharon}, biburl = {https://www.bibsonomy.org/bibtex/2c061ca5d7d0844b2f5a430def9982456/t.uemura}, description = {Definable groups for dependent and 2-dependent theories}, interhash = {3638e09c060a69ae90bb317b85a9c060}, intrahash = {c061ca5d7d0844b2f5a430def9982456}, keywords = {model theory}, note = {cite \href{http://arxiv.org/abs/math/0703045}{arxiv:math/0703045}}, timestamp = {2014-11-20T01:44:56.000+0100}, title = {Definable groups for dependent and 2-dependent theories}, url = {http://arxiv.org/abs/math/0703045}, year = 2007 }