I insist. That kind of sentence is wrong. In FOL + ZFC we can express the 
least-upper-bound property for real numbers. Maybe in FOL+ Real if Real is 
a system of axioms of real numbers we cannot. But at last we must stop 
giving this kind of example without specifying the axiomatic added to FOL. 


Ah! Yes. They specify the area. But it's barely visible, and even less 
decodable.

-- 
FL

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