Are there any examples other than using dimension for vector spaces where the easiest way to show that two objects are isomorphic is by using a classification theorem and showing that they must both be in the same class? (homeomorphisms count too)
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$\begingroup$ Finite sets, of course. $\endgroup$– Qiaochu YuanAug 3, 2010 at 3:33
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1$\begingroup$ Finite fields, algebraically closed fields, Hilbert spaces. $\endgroup$– Kevin VentulloAug 3, 2010 at 5:02
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3$\begingroup$ I have a hard time understanding this question. Metamathematically speaking, isn't that a standard situation? Typically, a classification scheme (if available) involves constructing a robust set of invariants and isomorphism of two general objects is checked by computing and comparing them. $\endgroup$– Victor ProtsakAug 3, 2010 at 5:05
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$\begingroup$ That's not the situation for isomorphism of groups given by presentations. $\endgroup$– Ryan BudneyAug 3, 2010 at 18:11
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