Borovik-Poizat rank and stability

Jeffrey Burdges; Gregory Cherlin

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arXiv · 0711.4040

Borovik-Poizat rank and stability

Jeffrey Burdges·Gregory Cherlin

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Abstract

There is an axiomatic treatment of Morley rank in groups, due to Borovik and Poizat. These axioms form the basis of the algebraic treatment of groups of finite Morley rank which is common today. There are, however, ranked structures, i.e. structures on which a Borovik-Poizat rank function is defined, which are not $\aleph_0$-stable. Poizat raised the issue of the relationship between this notion of rank and stability theory in the following terms: ``un groupe de Borovik est une structure stable, alors qu'un univers rangé n'a aucune raison de l'être ...''. Nonetheless, we show that a ranked structure is superstable.

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BibTeX RIS

Jeffrey Burdges, Gregory Cherlin. 2007-11-26. Borovik-Poizat rank and stability. https://arxiv.org/abs/0711.4040

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