Subject: FOM: Boolean algebra vs Boolean ring

Stephen G Simpson simpson at
Thu Mar 12 13:21:53 EST 1998

Vaughan Pratt writes:
 > >Does it mean that you don't distinguish basic operations
 > >from derived ones?
 > When appropriate.  In the class notes for my course "Algebra for Computer
 > Scientists" I establish necessary and sufficient conditions for a Boolean
 > basis to be complete, where the distinction clearly matters.

OK, good.  So your categorical perspective does not prevent you from
distinguishing basic operations from derived operations, provided
somebody can convince you that the distinction "clearly matters".
We are making progress, perhaps.

 > >So you are saying that, according to Sikorski, U
 > >is one of the operations of a Boolean ring,
 > Yes.

OK.  But do you accept my claim that U is a derived operation of
Boolean rings, not a basic operation of Boolean rings?  Or is this one
of the cases where you don't think the distinction "clearly matters"
and you are therefore refusing to acknowledge it?

 > I think from these answers it should be clear what my answers to your
 > other questions would have been, but I won't mind if you want to ask
 > any of them again.

No Vaughan, it's not clear, and I'd appreciate it if you would go back
and answer my other questions, rather than waiting for me to ask them
all again.  I think all of these answers can possibly play a role in
establishing a basis for rational discussion.  Are you interested in
establishing a basis for rational discussion?

-- Steve

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