Lovely pairs of models

Itay Ben-Yaacov, Anand Pillay, Evgueni Vassiliev
2003 Annals of Pure and Applied Logic  
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 (that is when the notion of a lovely pair is "axiomatizable"), ÿnding an analog of the nonÿnite cover property for simple theories. We show that, under these hypotheses, TP is also simple, and we
more » ... 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 T + P of TP, are lovely pairs, and "simple Robinson universal domains".
doi:10.1016/s0168-0072(03)00018-6 fatcat:lwmoglsjsjhxvd25vewo5isucu