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The generalized continuum hypothesis is equivalent to the generalized maximization principle

In spite of the work of Gödel and Cohen, which showed the undecidability of the Generalized Continuum Hypothesis (GCH) from the axioms of set theory, the problem still remains to decide GCH on the basis of new axioms. It is almost 100 years since Cantor first conjectured the Continuum Hypothesis, yet we seem to be no closer to determining its truth (or falsity). Nevertheless, it is a sound methodological principle that given any undecidable set-theoretical statement, we should search for “other (hitherto unknown) axioms of set theory which a more profound understanding of the concepts underlying logic and mathematics would enable us to recognize as implied by these concepts” (see Gödel [7, p. 265]).