Characterization of some theories preserved by localization

Lucas, Thierry;Lavendhomme, René
(1985) Annales de la Société Scientifique de Bruxelles —

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  • Lucas, ThierryUCLouvain
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  • Lavendhomme, RenéUCLouvain
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Abstract
(en) It is well-known that homogeneous equations are preserved by localization. The aim of this note is to prove a converse: for a broad class of theories T, T is preserved by localization if and only if T is "homogeneous-axiomatizable". From a logical point of view, this result is a very elementary but non-traditional application of the compactness theorem. From an algebraic point of view, it throws some light on the problem: what is preserved by localization?

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Lucas, T., & Lavendhomme, R. (1985). Characterization of some theories preserved by localization. Annales de la Société Scientifique de Bruxelles. https://hdl.handle.net/2078.5/55893