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The Generalized Continuum Hypothesis revisited

Saharon Shelah
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Abstract

We argue that we solved Hilbert's first problem positively (after reformulating it just to avoid the known consistency results) and give some applications. Let lambda to the revised power of kappa, denoted lambda^{[kappa]}, be the minimal cardinality of a family of subsets of lambda each of cardinality kappa such that any other subset of lambda of cardinality kappa is included in the union of aleph_0, (for all theta = mu for some kappa lambda^{[theta]}= lambda and (b) there is a family P of lambda subsets of lambda each of cardinality < mu such that every subset of lambda of cardinality mu is equal to the union of < kappa members of P .

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Saharon Shelah. 1998-09-15. The Generalized Continuum Hypothesis revisited. https://arxiv.org/abs/math/9809200

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