A Hanf number for saturation and omission: the superstable case
John T. Baldwin, Saharon Shelah · Mathematical logic quarterly · 2014
Suppose is a triple of two theories in vocabularies with cardinality λ, and a τ1-type p over the empty set that is consistent with T1. We consider the Hanf number for the property “there is a model M1 of T1 which omits p, but is saturated”. In [2], we showed that this Hanf number is essentially equal to the Löwenheim number of second order logic. In this paper, we show that if T is superstable, then the Hanf number is less than .