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Preprint Number 1760
1760. Erik Walsberg Dp-minimal expansions of (ℤ,+) via dense pairs via Mordell-Lang E-mail: Submission date: 15 April 2020 Abstract: This is a contribution to the classification problem for dp-minimal expansions of (ℤ,+). Let S be a dense cyclic group order on (ℤ,+). We use results on dense pairs to construct uncountably many dp-minimal expansions of (ℤ,+,S). These constructions are applications of the Mordell-Lang conjecture and are the first examples of non-modular dp-minimal expansions of (ℤ,+). We canonically associate an o-minimal expansion R of (ℝ,+,×), an R-definable circle group ℍ, and a character ℤ → ℍ to a non-modular dp-minimal expansion of (ℤ,+,S). We also construct a non-modular dp-minimal expansion of (ℤ,+,Val_p) from the character ℤ → ℤp^×, k ↦ exp(pk). Mathematics Subject Classification: Keywords and phrases: |
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