Re: clarification on recursively enumerable (R.E.)

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 11/10/04 

Date: Wed, 10 Nov 2004 16:22:13 +0100

David C. Ullrich wrote:
> <harrisq@tcs.inf.tu-dresden.de> wrote:
>>David C. Ullrich wrote:
>>
>>>Uh, no, in fact the set of theorems is never finite.
>>>(For example if A is an axiom then A, A&A, A&A&A, etc
>>>are all theorems).
>>
>>Just to be pedantic, you could have a set of axioms using no
>>variables. Boring, but possible.
>
> I'm not sure what your point is - there are no variables
> necessarily involved in the example I gave.

OK. Right.

My point (as small as it may be) was that you said that the set of
theorems is -never- finite and I thought that was too extreme; what I
said though was not even wrong. What I meant to say was that the
-rules of inference- might have no variables (or be empty).

My intuition was that the OP was considering r.e. sets, which of
course can be finite or not. 

-- 
Mitch Harris
(remove q to reply)

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