%0 Journal Article
%T Models of expansions of N with no end extensions
%A Saharon Shelah
%J Mathematics
%D 2008
%I arXiv
%X We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of N such that expanding N by any uncountably many of them suffice. Also we find arithmetically closed A with no definably closed ultrafilter on it.
%U http://arxiv.org/abs/0808.2960v2