Finitely generated submodels of an uncountably categorical homogeneous structure

We generalize the result of non-finite axiomatizability of totally categorical first-order theories from elementary model theory to homogeneous model theory. In particular, we lift the theory of envelopes to homogeneous model theory and develope theory of imaginaries in the case of ω-stable homogeneous classes of finite U-rank. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)