### Hanf number for the strictly stable cases

by Shelah. [Sh:1048]

Suppose bold {t} = (T, T_1, p) is a triple of two theories
in vocabularies tau subset tau_1 of cardinality lambda and
a tau_1-type p over the empty set: here we fix T and assume
it is stable. 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 larger than the Hanf number of
L_{lambda^+, kappa}
but smaller than the Hanf number of L_{(2^lambda)^+, kappa}
when T is stable with kappa = kappa (T) .

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