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True or false?

All closed and bounded intervals of definably complete ordered groups are definably compact.

Let $G$ be an ordered abelian group. Then, a definable subset $D ⊆ G$ is said to be definably compact if for every definable open cover $\{ϕ(a, G)\}_{a∈G}$ of $D$, there exists a pseudo-finite sub-cover $\{ϕ(a, G)\}_{a∈P}$ for some pseudo-finite set $P = ψ(t_0, G)$.

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  • $\begingroup$ I think it’d be clearer to say: “...there exists a sub-cover $\{\phi(a,G)\}_{a\in P}$ indexed by a definable closed bounded and discrete set $P$”. (Alternatively, if I’m not understanding pseudo-finiteness correctly, that’s worth clarifying in the question!) $\endgroup$ – Matt F. Mar 14 '18 at 3:37

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