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Oct 29, 2022 at 12:04 comment added Joel David Hamkins Your conjecture about finite/cofinite is not true, since for any given nontrivial element $b$, the set $\{x\mid x\leq b\}$ is definable from $b$ but it is neither finite nor cofinite. The definable sets, however, as I explained in my answer, are finite Boolean combinations of such trivial cones, whose vertices are the points in the finite Boolean algebra generated by the parameters, as I mention in my answer.
Oct 29, 2022 at 9:52 comment added Gerry Myerson Please edit n a link to the question on m.se, and put a link to this question there.
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Oct 28, 2022 at 2:30 answer added Joel David Hamkins timeline score: 11
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