Definable Groups for Dependent and 2-dependent Theories
نویسنده
چکیده
Let T be a (first order complete) dependent theory, C a κ̄-saturated model of T and G a definable subgroup which is abelian. Among subgroups of bounded index which are the union of < κ̄ type definable subsets there is a minimal one, i.e. their intersection has bounded index. See history in [Sh:876]. We then deal with definable groups for 2-dependent theories, a wider class of first order theories proving that for many pairs (M,N) of models the minimal bounded subgroup definable over M∪N is the intersection of the minimal ones for M and for N . Date: August 19, 2014. 1991 Mathematics Subject Classification. Primary 03E17; Secondary: 03E05, 03E50.
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