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Nam Nguyen wrote:
> ZF(C), after all, is just one theory out of infinite number
> of 1st order ones. (Formally, FOL framework never insists that
> we have to know about ZFC to formalize a different theory.)
>
> Assuming we've formalized a theory G of "geometry", how could we prove
> that the 5th "postulate" - as an axiom - is unprovable in G, without
> mentioning anything about ZF(C)? In other words, how could we possibly
> come up with a specific model of G in which the 5th is false? Thanks.
What's all this about axioms being proveable in a system? I've never
heard of such a system - how does that work?
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