Israel Journal of Mathematics

, Volume 230, Issue 2, pp 745–769 | Cite as

Mekler’s construction and generalized stability

  • Artem ChernikovEmail author
  • Nadja Hempel


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 ∈ N, and that NTP2 is preserved. We apply this result to obtain first examples of strictly k-dependent groups (with no additional structure).


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© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California Los AngelesLos AngelsUSA

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