# 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. DOI: 10.1002/malq.201300022 MR: 3274973 -
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.

- 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} }