Peano's Parlour

This site is dedicated to open problems in nonstandard models of Paeno Arithmetic and related theory. As in most areas, we do not suffer from a shortage of open problems. The problems are arranged by category. Here is the list of categories.

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 Schmerl, James H. Infinite substructure lattices of models of Peano arithmetic. J. Symbolic Logic 75 (2010), no. 4, 1366–1382 has a list of 20 questions with comments and references. Here is an errata for the book.