Submission date: 19 November 2008.

Abstract:

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.

Mathematics Subject Classification: 03C45, 03C64

Keywords and phrases: rosy theories, lovely pairs, dense pairs, dependent theories, strongly dependent theories.

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