[FOM] foundations meeting/FOMUS/discussion

martdowd at aol.com martdowd at aol.com
Fri Mar 25 10:32:26 EDT 2016

 Bruno Bentzen writes:

It turns out that in practice mathematicians often identify two structures whenever they are isomorphic.



This is only partly true.  Dedekind's and Cantor's construction of the real numbers yield isomorphic structures (although the isomorphism itself is a mathematically interesting object; also, the definition of isomorphism is set-theoretic).  On the other hand, the definition of a Galois group involves distinguishing isomorphic but unequal structures.

HOTT provides some interesting perspectives on isomorphism, but for foundational (and practical) use the set-theoretic definition is the "bottom line".

- Martin Dowd
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