[FOM] Bourbaki's general theory of isomorphism
viktormakarov at hotmail.com
Wed Jun 23 14:00:44 EDT 2010
A year ago there was a discussion on FOM "When is it appropriate to treat isomorphism as identity?" But the discussion went away without an answer.
It seems that an answer follows from the general theory of isomorphism suggested by Bourbaki in their book "Theory of sets".
If A is equal to B then, by Leibniz Law, every property of A is the same property of B.
If A is isomorphic to B, then every transportable property of A is the same property of B.
A property of A is transportable iff it preserved under all isomorphisms from A.
There is a paper by Victoria Marshall and Rolando Chuaqui "Sentences of Type Theory: the only sentences preserved under isomorphisms" - JSL, vol. 56, N3, Sep. 1991
More information about the FOM