On the category of models of a complete theory

Publisher： Cambridge University Press

E-ISSN： 1943-5886|47|2|249-266

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.47, Iss.2, 1982-06, pp. : 249-266

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Abstract

Let T be a countable complete theory and C(T) the category whose objects are the models of T and morphisms are the elementary maps. The main object of this paper will be the study of C(T). The idea that a better understanding of the category may give us model theoretic information about T is quite natural: The (semi) group of automorphisms (endomorphisms) of a given structure is often a powerful tool for studying this structure. But certainly, one of the very first questions to be answered is: “to what extent does this category C(T) determine T?”

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