Geodesic
A remark on accessible and axiomatizable categories
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 2, pp. 411-414.

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For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle.
Classification : 03C99, 18B99
Keywords: accessible category; infinitary logic; Vopěnka's principle 
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Adámek, Jiří; Rosický, Jiří. A remark on accessible and axiomatizable categories. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 2, pp. 411-414. http://geodesic.mathdoc.fr/item/CMUC_1996__37_2_a19/