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Feb 27, 2019 at 16:35 comment added Noah Schweber @ColinTan More simply, your structure is an expansions-by-definitions of a definable substructure of $(\mathbb{R}; +,\times)$, and so o-minimality immediately follows.
Feb 27, 2019 at 14:59 comment added Colin Tan So by the same argument, also the nonnegative reals $[0, \infty) $ is o-minimal, right? Thank you, James!
Feb 27, 2019 at 5:02 history answered James CC BY-SA 4.0