The independence property in generalized dense pairs of structures. (English) Zbl 1220.03014

Berenstein, Alexander; Dolich, Alf; Onshuus, Alf

J. Symb. Log. 76, No. 2, 391-404 (2011).

Summary: We provide a general theorem implying that for a (strongly) dependent theory \(T\) the theory of sufficiently well-behaved pairs of models of \(T\) is again (strongly) dependent. We apply the theorem to the case of lovely pairs of thorn-rank-one theories as well as to a setting of dense pairs of first-order topological theories.

MSC:

03C45

Classification theory, stability, and related concepts in model theory

Keywords:

rosy theories; lovely pairs; dense pairs; dependent theories; strongly dependent theories

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