Mekler's construction and generalized stability

Artem Chernikov; Nadja Hempel

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arXiv · 1708.03724

Mekler's construction and generalized stability

Artem Chernikov·Nadja Hempel

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Abstract

Mekler's construction gives an interpretation of any structure in a finite relational language in a group (nilpotent of class $2$ and exponent $p>2$, but not finitely generated in general). Even though this construction is not a bi-interpretation, it is known to preserve some model-theoretic tameness properties of the original structure including stability and simplicity. We demonstrate that $k$-dependence of the theory is preserved, for all $k \in \mathbb{N}$, and that NTP$_2$ is preserved. We apply this result to obtain first examples of strictly $k$-dependent groups (with no additional structure).

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Artem Chernikov, Nadja Hempel. 2017-08-11. Mekler's construction and generalized stability. https://arxiv.org/abs/1708.03724

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