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.
@article{118845, author = {Ji\v r\'\i\ Ad\'amek and Ji\v r\'\i\ Rosick\'y}, title = {A remark on accessible and axiomatizable categories}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {37}, year = {1996}, pages = {411-414}, zbl = {0849.18005}, mrnumber = {1399015}, language = {en}, url = {http://dml.mathdoc.fr/item/118845} }
Adámek, Jiří; Rosický, Jiří. A remark on accessible and axiomatizable categories. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 411-414. http://gdmltest.u-ga.fr/item/118845/
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