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``Re: nomenclature'' by jihemme on 2002-06-03 20:26:00
This is standart nomenclature. In some other books or references, the term "model" is also used for structures. The term "model theory" comes from the notion of satisfaction : when we write the symbol A|= phi, we read "A models phi" or "A is a model of phi".

Usually, when the term "model" is used for a "structure", the author means a "structure" that "models" a bunch of formulas. I hope this is clear.
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