Lovely pairs of models

Annals of Pure and Applied Logic 122 (1-3):235-261 (2003)
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Abstract

We introduce the notion of a lovely pair of models of a simple theory T, generalizing Poizat's “belles paires” of models of a stable theory and the third author's “generic pairs” of models of an SU-rank 1 theory. We characterize when a saturated model of the theory TP of lovely pairs is a lovely pair , finding an analog of the nonfinite cover property for simple theories. We show that, under these hypotheses, TP is also simple, and we study forking and canonical bases in TP. We also prove that assuming only that T is low, the existentially universal models of the universal part of a natural expansion TP+ of TP, are lovely pairs, and “simple Robinson universal domains”

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Citations of this work

On lovely pairs of geometric structures.Alexander Berenstein & Evgueni Vassiliev - 2010 - Annals of Pure and Applied Logic 161 (7):866-878.
An independence theorem for ntp2 theories.Itaï Ben Yaacov & Artem Chernikov - 2014 - Journal of Symbolic Logic 79 (1):135-153.
Dimensions, matroids, and dense pairs of first-order structures.Antongiulio Fornasiero - 2011 - Annals of Pure and Applied Logic 162 (7):514-543.
Dense codense predicates and the NTP 2.Alexander Berenstein & Hyeung-Joon Kim - 2016 - Mathematical Logic Quarterly 62 (1-2):16-24.

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
Positive model theory and compact abstract theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (01):85-118.
Paires de structures Stables.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (2):239-249.
Generic pairs of SU-rank 1 structures.Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 120 (1-3):103-149.
The number of types in simple theories.Enrique Casanovas - 1999 - Annals of Pure and Applied Logic 98 (1-3):69-86.

View all 11 references / Add more references