Hanf number for the strictly stable cases
Logic
2019-02-07 v4
Abstract
Suppose t = (T,T_1, p) is a triple of two theories T subset T_1 in vocabularies tau subset tau_1 (respectively) of cardinality lambda and a tau_1-type p over the empty set; in the main case here is with T stable. We show the Hanf number for the property: "there is a model M_1 of T_1 which omits p, but M_1 restricted to 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). In fact, we characterize the Hanf number of t when we fix (T, lambda) where T is a first order complete, lambda > |T| and demand |T_1| < lambda.
Cite
@article{arxiv.1412.0428,
title = {Hanf number for the strictly stable cases},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:1412.0428},
year = {2019}
}