Geodesic
Elementarity and Dimensions
Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 292-298.

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An alternative proof of Fedorchuk's recent result that $\dim X\le\operatorname{Dg}X$ for compact Hausdorff spaces X is given. The problem is reduced to the metric case by using the Lowenheim–Skolem theorem. 
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K. P. Hart. Elementarity and Dimensions. Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 292-298. http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a14/

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