Peano's Parlour

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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.

Cuts in models of PA and independence results.

Recursively saturated, resplendent models, and saturated models.

Standard systems and the Scott set problem.

Lattices of elementary substructures.

Uncountable models with interesting second-order properties.

Nonstandard satisfaction classes.

Complexity and classification of countable models.

Automoprhism groups.

Model theory of strong fragments of arithmetic.

Model theory of weak fragments of arithmetic.

Model theoretic methods in proof theory.

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 To contribute without registering, send an email to Victoria Gitman or to Roman Kossak at