Uncountable categoricity for gross models

Michael C. Laskowski, Anand Pillay
2004 Proceedings of the American Mathematical Society  
A model M is said to be gross if all infinite definable sets in M have the same cardinality (as M ). We prove that if for some uncountable κ, T has a unique gross model of cardinality κ, then for any uncountable κ, T has a unique gross model of cardinality κ.
doi:10.1090/s0002-9939-04-07451-9 fatcat:xcedc2fnkna3zc64mo6m7hbooy