Uncountable categoricity for gross models
Michael Chris Laskowski, Anand Pillay · Proceedings of the American Mathematical Society · 2004
A model M M is said to be gross if all infinite definable sets in M M have the same cardinality (as M M ). We prove that if for some uncountable κ \kappa , T T has a unique gross model of cardinality κ \kappa , then for any uncountable κ \kappa , T T has a unique gross model of cardinality κ \kappa .