## Journal of Symbolic Logic

### Finitary Sketches

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745293

Mathematical Reviews number (MathSciNet)
MR1472119

Zentralblatt MATH identifier
0885.18001

JSTOR