Much of model theory of arithmetic can be seen as results about structures of the form (M,omega), where M is a nonstandard model of PA and omega is its standard cut. Our joint work in [1] resulted from an attempt to develop a more systematic study arithmetic in the language with the standardness predicate.

In the talk, I will give a survey of results and I will outline some proofs.

[1] Richard Kaye, Roman Kossak, Tin Lok Wong, Adding standradness to nonstandard models}, in Studies in Weak Arithmetics, edited by Patrick Cegielski, Charalampos Cornaros, and Constantin Dimitracopoulos, CSLI lecture notes; no. 196, pp. 179 - 198, 2013.