Is the name "model" as used in model theory the same thing as the "model" used in geometry (e.g. the models of hyperbolic geometry)?
And is it possible to say that different probability spaces which induce the same distribution are "different models" of a random variable?
Confusion: It seems somewhat plausible, since Alfred Tarski was strongly connected with both senses of the word (at least for Euclidean geometry). On the other hand, the Wikipedia article about model theory is to me more confusing than helpful, giving statements like "model theory = algebraic geometry - fields" or "universal algebra + logic = model theory", when the opening paragraph seems to give a much more general description of what model theory is, one which would seem to also apply to fields like differential geometry or analysis: "A set of sentences in a formal language is called a theory; a model of a theory is a structure (e.g. an interpretation) that satisfies the sentences of that theory."