# Sh:992

• Baldwin, J. T., & Shelah, S. (2014). A Hanf number for saturation and omission: the superstable case. MLQ Math. Log. Q., 60(6), 437–443.
• Abstract:
Suppose {\bf t} =(T,T_1,p) is a triple of two theories in vocabularies \tau \subset \tau_1 with cardinality \lambda 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 less than \beth_{({2^{{(2^{ \lambda})}^+}}){}^{^+}} if T is superstable. If T is required only to be stable, the Hanf number is bounded by the Hanf number of L_{(2^\lambda)^+,\kappa(T)}.

We showed in an earlier paper that without the stability restriction the Hanf number is essentially equal to the Löwenheim number of second order logic.

• Version 2014-04-24_11 (10p) published version (8p)
Bib entry
@article{Sh:992,
author = {Baldwin, John T. and Shelah, Saharon},
title = {{A Hanf number for saturation and omission: the superstable case}},
journal = {MLQ Math. Log. Q.},
fjournal = {MLQ. Mathematical Logic Quarterly},
volume = {60},
number = {6},
year = {2014},
pages = {437--443},
issn = {0942-5616},
mrnumber = {3274973},
mrclass = {03C45 (03C75 03C85)},
doi = {10.1002/malq.201300022}
}