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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