A Hanf number for saturation and omission

by Baldwin and Shelah. [BlSh:958]
Fundamenta Math, 2011
Suppose {mathbf T} =(T,T_1,p) is a triple of two countable theories in languages tau subset tau_1 and a tau_1-type p over the empty set. We show the Hanf number for the property: There is a model M_1 of T_1 which omits p, but M_1 restriction tau is saturated is at least the L{o}wenheim number of second order logic.

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