Countable imaginary simple unidimensional theories

TL;DR

This paper proves that countable simple unidimensional theories eliminating hyperimaginaries are supersimple, resolving a longstanding problem in the theory of simple models under minimal assumptions.

Contribution

It establishes a significant link between simplicity, unidimensionality, and supersimplicity in countable theories, extending Shelah's problem to broader contexts.

Findings

Countable simple unidimensional theories are supersimple.

Elimination of hyperimaginaries is crucial for supersimplicity.

The result applies under weak assumptions, broadening previous scope.

Abstract

We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.