A general condition for collapse results
Abstract In Belegradek et al. (Ann. Pure Appl. Logic 97 (1–3) (1999) 85) the collapse result theorem was proved for locally generic queries over ordered domain with pseudo-finite homogeneity property. In a very interesting paper of Baldwin and Benedikt (Stability theory, permutations of indiscernibles, and embedded finite models, preprint, 1998) the collapse result theorem was proved for locally generic queries over ordered domains without the independence property. It means that over such a domain, order-generic extended queries fail to express more than restricted queries. It was observed by Baldwin and Benedikt (1998) that any theory without the independence property is P -reducible. I prove that, for the P -reducible theories, a version of pseudo-finite homogeneity property holds.