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May 15, 2019 at 5:14 comment added James E Hanson A first-order theory of some structure with a linear order (such as the theory of the structure $(\mathbb{R},0,1,+,\cdot,\leq)$ is O-minimal if every definable set (with parameters) is equal to some finite union of intervals (of possibly infinite or zero length). This is almost certainly not the most elementary proof possible, but that's usually the case when you use a powerful general theorem like the fact that $\mathrm{RCF}$ is O-minimal.
May 15, 2019 at 0:26 comment added VS. What is O-minimality and is this the most elementary proof possible?
May 13, 2019 at 17:40 history answered James E Hanson CC BY-SA 4.0