Ultraproducts and Model Theory
نویسنده
چکیده
The first-order model-theoretic description of mathematical structures is unable to always uniquely characterize models up to isomorphism when the models are not finite. In this paper I look to ultraproducts of models to remedy this somewhat. By taking the ultraproduct construction over models, we form a new model out of many that preserves all of the first-order logical sentences of “most” of the original models. This construction will be useful for characterizing when models are equivalent according to their first-order model-theoretic description, and for describing the class of models that are equivalent in this way.
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