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Elementary categories. (English) Zbl 0665.18004

The paper contributes to the problem of characterizing categories of models of usual one-sorted finitary first-order theories. Any locally finitely presentable category with a finitely presentable generator is of this kind. Surprisingly, the same is true for any category of many-sorted sets. (This result was further developed by G. Jarzembski [Finitary fibrations, Cah. Topologie Géom. Differ. (to appear)].) Finally, Bankston’s conjecture is proved (independently of B. Banaschewski [Can. J. Math. 36, 1113-1118 (1984; Zbl 0561.18004)]).
Reviewer: J.Rosický

MSC:

18A99 General theory of categories and functors
03C68 Other classical first-order model theory
18B99 Special categories

Citations:

Zbl 0561.18004
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References:

[1] B. Banaschewski, More on compact Hausdorff spaces and finitary duality. Canad. J. Math.36, 1113-1118 (1984). · Zbl 0561.18004 · doi:10.4153/CJM-1984-063-6
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[11] M. Makkai andR. Par?, Accessible categories: The foundations of categorical model theory. Dept. Math. McGill Univ., Montreal 1987.
[12] M. Makkai andA. M. Pitts, Some results on locally finitely presentable categories. Trans. Amer. Math. Soc.229, 473-496 (1987). · Zbl 0615.18002 · doi:10.1090/S0002-9947-1987-0869216-2
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