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In 1922, Fraenkel and Skolem pointed out that Zermelo's axioms cannot prove the existence of the set {Z0, Z1, Z2, … } where Z0 is the set of natural numbers, and Zn+1 is the power set of Zn.
The Fifth Empire (Portuguese: Quinto Império) is a concept of a global Portuguese empire with spiritual and temporal power, set to take its place in a new era and based in the prophecy of the second chapter of the Book of Daniel and in the Book of Revelation, whose origins lay with António Vieira.