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``Re: nomenclature'' by jihemme on 2002-06-04 11:13:50
note that you have used "model of a theory" in your question. A "countable model of set theory" is a countable structure which is a model of the axioms of set theory.

Sometimes I've seen "model" used for "structure", especially when we are talking about structures that are models of a theory.

Just to give you a quick example, any graph is a structure for the signature of set theory, but to get a model of set theory, you must have more than a mere graph.
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