Finitary Sketches

Abstract

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.

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Cite this paper

@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} }