FOM: poll

Kanovei kanovei at
Mon Feb 2 06:15:09 EST 1998

<Date: Sun, 01 Feb 1998 13:47:42 -0800
<From: Vaughan Pratt <pratt at>

<You seem to be arguing that you can put group structure on an "anonymous"
<set (one defined only up to isomorphism) but not topological structure.[....]

I argue that 

1) groups are concrete sets with the group operation, 
there are also isomorphism classes of them, and, if 
you want to include some extra structure (e.g. topology) 
to groups (and isomorphisms) this does not change the picture, 

2) what is said in 1) is commonly known (both among the 
near 300 fom-ers and among the whole mathematical community), 

3) if someone wants (for the sake of simplicity) to call 
isomorphism classes of groups by simply groups he is 
welcome to do so, and in this sense there are just two 
groups of order 4,

4) what is said above is so elementary that any attempt 
to play this into a foundational system is ridiculous. 

Vladimir Kanovei

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