Submission date: 17 march 2019

Abstract:

Mekler constructed a way to produce a pure group from any given structure where the construction preserves κ-stability for any cardinal κ. Not only the stability, it is known that his construction preserves various model-theoretic properties such as simplicity, NIP, and NTP_2. Inspired by the last result, we show that the construction also preserves NTP_1(NSOP_2) and NSOP_1. As a corollary, we obtain that if there is a theory of finite language which is non-simple NSOP_1, or which is NSOP_2 but has SOP_1, then there is a pure group theory with the same properties, respectively.

Mathematics Subject Classification: 03C45, 05C25

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Full text arXiv 1903.07087: pdf, ps.