English

Models of PA: Standard Systems without Minimal Ultrafilters

Logic 2018-01-16 v3

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).

Keywords

Cite

@article{arxiv.0901.1499,
  title  = {Models of PA: Standard Systems without Minimal Ultrafilters},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:0901.1499},
  year   = {2018}
}