Freeness in classes without equality

Publisher: Cambridge University Press

E-ISSN: 1943-5886|64|3|1159-1194

ISSN: 0022-4812

Source: The Journal of Symbolic Logic, Vol.64, Iss.3, 1999-09, pp. : 1159-1194

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Abstract

This paper is a continuation of [27], where we provide the background and the basic tools for studying the structural properties of classes of models over languages without equality. In the context of such languages, it is natural to make distinction between two kinds of classes, the so-called abstruct classes, which correspond to those closed under isomorphic copies in the presence of equality, and the reduced classes, i.e., those obtained by factoring structures by their largest congruences. The generic problem described in [27] is to investigate under what conditions this reduction process does not alter the metatheory of a class.