A description of autostable models

Models that are uniformly autostable in various senses are studied. The general criterion of autostability is cited, and we argue that it cannot be transposed into a general sufficient condition of autostability. We establish model-theoretic criteria of autostability in degree 0′, both for the whole class of recursive models and some of its main subclasses. Supported by RFFR grant No. 096-01-01525. Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 26–36, January–February, 1997.