A note on effective ultrapowers: Uniform failure of bounded collection

By suitably adapting an argument of Hirschfeld (see [2, Chapter 9]), we show that there is a single Δ 1 formula that defeats “bounded collection” for any model of II 2 Arithmetic that is either a recursive ultrapower or an existentially complete model. Some related facts are noted. MSC: 03F30, 03C62.