FOM: Boolean algebra vs Boolean ring

Vaughan Pratt pratt at cs.Stanford.EDU
Wed Mar 11 13:01:24 EST 1998

>From Colin McLarty(cxm7 at 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

From: Bill Tait
>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).

That's for elementary theories, not algebraic.

Vaughan Pratt

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