Elimination of Hyperimaginaries and Stable Independence in simple CM-trivial theories

TL;DR

This paper explores the elimination of hyperimaginaries and the stability of independence in simple CM-trivial theories, showing that hyperimaginaries can be interbounded with finitary ones and that stability arises in supersimple cases.

Contribution

It proves that in simple CM-trivial theories, hyperimaginaries are interbounded with finitary hyperimaginaries and that such theories eliminate hyperimaginaries if they eliminate finitary ones.

Findings

Hyperimaginaries are interbounded with finitary hyperimaginaries in simple CM-trivial theories.

Elimination of hyperimaginaries occurs if finitary hyperimaginaries are eliminated.

Independence is stable in supersimple CM-trivial theories.

Abstract

In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable.