Note on two theorems of Mostowski

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Abstract
The present note is conceived as a sequel to Mostowki's paper, Über die Unabhängigkeit des Wohlordnungssatzes vom Ordnungsprinzip (which will be quoted as “M.”).In that paper Mostowski considers a system of axioms , very close to the system of axiomatic set theory of Bernays, but where the axiom of choice is not supposed to hold. Mostowski proves that the well-ordering theorem (Wohlordnungssatz) cannot be derived from the system plus the principle of simple ordering (Ordnungsprinzip).

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