A model and its subset: the uncountable case

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Abstract

Assume Q is a definable subset of a model of T. We define a notion of Q-isolated type, generalizing an earlier definition for countable Q. This notion is absolute. For superstable T, we give some sufficient conditions for the existence of Q-atomic models. We apply this to prove some results on weak categoricity over a predicate.

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Research supported by KBN grant 2-1103-91-01.