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categoricity


Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


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L ogic Dewey 's term, although the idea is much older, for a semantic property ascribed to a theory or an axiomatic system, according to which any two of its satisfying interpretations (or models) are isomorphic. That is, any two models, M and N, of a theory T have the same structure, and there is a one-to-one correspondence between the domain of M and the domain of N. A theory with such a standard structure or model is categorical. Categoricity is an ideal property for the axiomatic method, but its application is very limited. “Categoricity, as thus defined for the first-order language x, is a relatively trivial notion. None of the usual axiomatically formulated mathematical theories will be categorical, because any set of sentences of x with an infinite model will have models that are of differing cardinality and hence are not isomorphic.” Mates, Elementary Logic ... log in or subscribe to read full text

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