- Published 1997 in J. Symb. Log.

Finitary sketches, i.e., sketches with nite-limit and nite-colimit specii-cations, are proved to be as strong as geometric sketches, i.e., sketches with nite-limit and arbitrary colimit speciications. Categories sketchable by such sketches are fully characterized in the innnitary rst-order logic: they are axiomatizable by-coherent theories, i.e., basic theories using nite conjunctions, countable disjunctions, and-nite quantiications. The latter result is absolute; the equivalence of geometric and nitary sketches requires (in fact, is equivalent to) the non-existence of measurable cardinals.

@article{Admek1997FinitaryS,
title={Finitary Sketches},
author={Jir{\'i} Ad{\'a}mek and Peter T. Johnstone and Johann A. Makowsky and Jir{\'i} Rosick{\'y}},
journal={J. Symb. Log.},
year={1997},
volume={62},
pages={699-707}
}