FOM: Boolean algebra vs Boolean ring
wtait at ix.netcom.com
Tue Mar 10 22:43:50 EST 1998
>From Colin McLarty(cxm7 at po.cwru.edu) 3/10:
> Now Vaughan, like many other logicians and mathematicians,
>understands an algebraic theory without distinguishing "basic"
>operations from "derived" ones--that is primitive from defined
>operations. There is nothing arcane about this, and on this
>basis Boolean algebras are exactly the same things as Boolean
I understand what you are saying, Colin; but you need to be explicit
about what you mean by `derived' operations. I assume you mean those that
are expressed by terms, which is ok. But if one takes it to mean
explicitly definable functions, then it would be wrong; since the
introduction of explicitly definable functions can destroy e.g.
uisomorphic embeddings (unless they are elementary embeddings).
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