Number fields and divisible groups via model theory. (English) Zbl 1496.11140
Summary: In this note, we first show that solutions of certain equations classify the number fields lying in imaginary quadratic number fields. Then, we study divisible groups with a predicate. We show that these structures are not simple and have the independence property under some natural assumptions.
MSC:
| 11U09 | Model theory (number-theoretic aspects) |
| 03C60 | Model-theoretic algebra |
| 03C45 | Classification theory, stability, and related concepts in model theory |
| 11R21 | Other number fields |
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