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On 18 Aug 2006 17:33:32 -0700, George Dance <georgedance04@xxxxxxxx>
said:
> ...
> What's all this about axioms being proveable in a system? I've never
> heard of such a system - how does that work?
In pretty much every mathematical logic text, a proof in an (axiomatic)
system S is defined to be a sequence of formulas (in the language of S),
each of which is either an axiom of S or follows from formulas occurring
earlier in the sequence by a rule of inference of S. A formula F is
said to provable in S if F is the formula occurring last in a proof in
S. Thus, trivially, for any axiom A of S, the 1-element sequence <A> is
a proof of A in S; so A is provable in S.
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