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On Wed, 25 Oct 2006, Atreides wrote:
> F is a set of sentences: { A_1, A_2, ...} s.t. {A_1 .. A_i} |/= A_i+1 (
> A_i+1 is not a logical consequence of previous A_i's).
|- means logical consequence, provable.
Do you mean not { A_1,.. A_i } |- A_(i+1) ?
> How to prove that F is NOT finite axiomatizable?
>
{ (Ex)~(x = x) } is a finite collection of statements that will prove
every statement in F.
> Any ideas or hints?
Does the set of axioms have to be consistent?
> Can we do something like this - get every finite T, add it's elements
> to F and suppose that this property still holds?
>
Isn't this equivalent to showing the theorems of a finite consistent set
of statements is finite? As I'm not psychic, you are not allowed to think
I know what logical system you're imagining.
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