Definable groups for dependent and 2-dependent theories

by Shelah. [Sh:886]

Let T be a (first order complete) dependent theory, {{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 <= 2^{|T|} . We then deal with 2-dependent theories, a wider class of first order theories.


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