This site is dedicated to open problems in nonstandard models of Peano Arithmetic and related theories. As in most areas of mathematics, we do not suffer from a shortage of open problems. The problems are arranged by topics.
The last chapter of The structure of models of Peano arithmetic by Kossak and Schmerl has a list of 20 questions with comments and references. Here is an errata for the book.
Contributing to Peano's Parlour
All registered members can contribute to problems/solutions/corrections/remarks. To register, send an email to the webmaster Victoria Gitman at email@example.com. To contribute without registering, send an email to Victoria Gitman or to Roman Kossak at firstname.lastname@example.org.