Submission date: 15 August 2017

Abstract:

Mekler's construction gives an interpretation of any structure in a finite relational language in a pure 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 further that k-dependence of the theory is preserved, for all k in N, and that NTP2 is preserved. We apply this result to obtain first examples of strictly k-dependent pure groups.

Mathematics Subject Classification: 03C45, 03C60, 20F18, 05C25

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Full text arXiv 1708.03724: pdf, ps.