  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.
