The Hanf number in the strictly stable case

摘要

We associate Hanf numbers H(t) to triples t = (T,T_1,p) where T and T_1 are theories and p is a type.We show that the Hanf number for the property: “there is a model M_1 of T_1 which omits p,but M_1|τ is saturated” is larger than the Hanf number of L_(λ+,κ) but smaller than the Hanf number of L_((2λ )+,κ) when T is stable with κ = κ(T ).In fact,surprisingly,we even characterise the Hanf number of t when we fix (T,λ) where T is a first order complete (and stable),λ ≥ |T| and demand |T_1| ≤ λ.