Quasiresolvent Models and $B$-Models

Relations among classes of resolvent, quasiresolvent, intrinsically enumerable models, and $B$-models are established. It is proved that every linear order containing a $\Delta$-subset isomorphic to $\omega$ or to $\omega^-$ is not quasiresolvent. It is stated that every model of a countably categorical theory is a $B$-model. And it is shown that for every $B$-model in a hereditarily finite admissible set, the uniformization theorem fails.