A family of dp-minimal expansions of \((\mathbb{Z}; +)\). (English) Zbl 1537.03047

Tran, Chieu-Minh; Walsberg, Erik

Notre Dame J. Formal Logic 64, No. 2, 225-238 (2023).

The present paper concerns studying expansions of the additive group of integers by a ternary relation of an additive cyclic order. The authors show that such expansions are dp-minimal. They also prove that one can produce continuum of dp-minimal expansions of the additive group of integers up to definable equivalence. Thus, the authors obtain a result, which refutes a supposition that there are not too many dp-minimal expansions of this group.

Reviewer: Beibut Kulpeshov (Almaty)

MSC:

03C65	Models of other mathematical theories
03C64	Model theory of ordered structures; o-minimality
03C10	Quantifier elimination, model completeness, and related topics
03C40	Interpolation, preservation, definability

Keywords:

dp-minimality; cyclic order; additive cyclic order; additive group of integers; expansion; VC1 property; Sturmian sequence

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