Lovely pairs of models Original Research Article

We introduce the notion of a lovely pair of models of a simple theory T, generalizing Poizatʹs “belles paires” of models of a stable theory and the third authorʹs “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 (that is when the notion of a lovely pair is “axiomatizable”), 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”.