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]]>I was under the impression that groups are models of group theory; and rings are models of the theory of rings.

Also, “model” outside of pure mathematics is not the same as “model” in pure mathematics. In pure mathematics, model usually means a structure satisfying a certain theory. Outside of it, a model is normally some collection of mathematical equations which seem to approximate a certain behaviour, or so. I’m sure someone can find the connection, but it is certainly not immediate and the same.

You can also make the claim that a model is showing new cloths and designer shoes, but is not a model theorist, that is also true.

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]]>The objects that group theorists study are groups. The object that ring theorists study are rings. The objects that measure theorists study are sets equipped with a measure. And so on. On the other hand, the objects that most modern set theorists study seem to be models of set theories, especially models and extensions of ZFC, as well as the consistency, strength, and independence of said axioms, rather than actual sets themselves. So the situation between group theory and set theory is different.

Actually, perhaps a better example against my original point would be string theory from mathematical physics. Modern string theorists, especially with the string landscape and the swampland program, study models of string theory, rather than strings themselves, yet aren’t considered model theorists.

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]]>Is a “group theorist” simply a model theorist who specialises in models of group theory?

No. And the same is true about set theorists. Set theorists are mathematicians who are interested in set theory. The techniques in set theory are not model theoretic in nature, not any more than the wreath product of two groups is model theoretic, or that “free group” is a model theoretic construction.

But unlike other subfields of mathematics, e.g. group theory, in set theory we simply use the term “model of set theory” in a more explicit way.

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]]>(And thanks in advance to all those who help getting the word around.)

]]>Yes! I’ve sat on it for a while to put some distance to the event.

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