Journal of Symbolic Logic

Finitary Sketches

J. Adamek, P. T. Johnstone, J. A. Makowsky, and J. Rosicky

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Finitary sketches, i.e., sketches with finite-limit and finite-colimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finite-limit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary first-order logic: they are axiomatizable by $\sigma$-coherent theories, i.e., basic theories using finite conjunctions, countable disjunctions, and finite quantifications. The latter result is absolute; the equivalence of geometric and finitary sketches requires (in fact, is equivalent to) the non-existence of measurable cardinals.

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J. Symbolic Logic, Volume 62, Issue 3 (1997), 699-707.

First available in Project Euclid: 6 July 2007

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Adamek, J.; Johnstone, P. T.; Makowsky, J. A.; Rosicky, J. Finitary Sketches. J. Symbolic Logic 62 (1997), no. 3, 699--707.

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