Models of arithmetic meet set theory and topology

The first part of the talk is expository and provides a general introduction to nonstandard models of arithmetic, and the various ways they interact with set theory and topology. 

The second part focuses on recent results obtained in collaboration with Joel David Hamkins and Bartosz Wcisło on models of arithmetic whose "numbers" carry a nontrivial topology with respect to which the addition and multiplication operations of the model are continuous; these results as presented in the following manuscript:
https://arxiv.org/abs/1808.01270