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Jiří Adámek [3]J. Adamek [2]
  1.  35
    On Quasivarieties and Varieties as Categories.Jiří Adámek - 2004 - Studia Logica 78 (1-2):7 - 33.
    Finitary quasivarieties are characterized categorically by the existence of colimits and of an abstractly finite, regularly projective regular generator G. Analogously, infinitary quasivarieties are characterized: one drops the assumption that G be abstractly finite. For (finitary) varieties the characterization is similar: the regular generator is assumed to be exactly projective, i.e., hom(G, –) is an exact functor. These results sharpen the classical characterization theorems of Lawvere, Isbell and other authors.
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  2.  23
    On the Logic of Continuous Algebras.Jiří Adámek, Alan H. Mekler, Evelyn Nelson & Jan Reiterman - 1988 - Notre Dame Journal of Formal Logic 29 (3):365-380.
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  3.  34
    Finitary Sketches.J. Adámek, P. T. Johnstone, J. A. Makowsky & J. Rosický - 1997 - Journal of Symbolic Logic 62 (3):699-707.
    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 σ-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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