Models of PA: Standard Systems without Minimal Ultrafilters

Abstract

We prove that bold N, the standard model of arithmetic, has an uncountable elementary extension N such that there is no ultrafilter on the Boolean Algebra of subsets of bold N represented in N which is minimal (i.e. as in Rudin-Keisler order for partitions represented in N).

References in corpus (1)

• Models of expansions of N with no end extensions