Peano's Parlour

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. Here is the list:

1. Cuts in models of PA and independence results

2. Recursively saturated, resplendent models, and saturated models.

3. Automorphisms and automorphism groups.

4. Standard systems and the Scott set problem.

5. Lattices of elementary substructures.

6. Uncountable models with interesting second-order properties.

7. Nonstandard satisfaction classes.

8. Model theory of strong fragments of arithmetic.

9. Model theory of weak fragments of arithmetic.

10. Model theoretic methods in proof theory.

The last chapter of Kossak, Roman; Schmerl, James H. The structure of models of Peano arithmetic. Oxford Logic Guides, 50. Oxford Science Publications. The Clarendon Press, Oxford University Press, Oxford, 2006. has a list of 20 questions with comments and references. Here is an errata for the book.