Definable groups for dependent and 2-dependent theories

Details Definable groups for dependent and 2-dependent theories Definable groups for dependent and 2-dependent theories

2007-03-01

arxiv.org/abs/math/0703045v4

Mathematics

Logic

Scientific paper

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.

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