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The independence property in generalized dense pairs of structures
Journal of Symbolic Logic 76 (2):391 - 404 (2011)
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 theoriesOther Versions
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Citations of this work
Expansions of o-minimal structures by dense independent sets.Alfred Dolich, Chris Miller & Charles Steinhorn - 2016 - Annals of Pure and Applied Logic 167 (8):684-706.
Companionability characterization for the expansion of an o-minimal theory by a dense subgroup.Alexi Block Gorman - 2023 - Annals of Pure and Applied Logic 174 (10):103316.
Expansions which introduce no new open sets.Gareth Boxall & Philipp Hieromyni - 2012 - Journal of Symbolic Logic 77 (1):111-121.
Fields with a dense-codense linearly independent multiplicative subgroup.Alexander Berenstein & Evgueni Vassiliev - 2020 - Archive for Mathematical Logic 59 (1-2):197-228.
Generic trivializations of geometric theories.Alexander Berenstein & Evgueni Vassiliev - 2014 - Mathematical Logic Quarterly 60 (4-5):289-303.
References found in this work
Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
Lovely pairs of models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.
On lovely pairs of geometric structures.Alexander Berenstein & Evgueni Vassiliev - 2010 - Annals of Pure and Applied Logic 161 (7):866-878.
Generic pairs of SU-rank 1 structures.Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 120 (1-3):103-149.
Review: C. C. Chang, H. J. Keisler, Model Theory. [REVIEW]Michael Makkai - 1991 - Journal of Symbolic Logic 56 (3):1096-1097.
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