The Generalized Continuum Hypothesis revisited

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Scopus citations

Abstract

We can reformulate the generalized continuum problem as: for regular κ < λ we have λ to the power κ is λ, We argue that the reasonable reformulation of the generalized continuum hypothesis, considering the known independence results, is "for most pairs κ < λ of regular cardinals, λ to the revised power of κ is equal to λ". What is the revised power? λ to the revised power of κ is the minimal cardinality of a family of subsets of λ each of cardinality κ such that any other subset of λ of cardinality κ is included in the union of strictly less than κ members of the family. We still have to say what "for most" means. The interpretation we choose is: for every λ, for every large enough κ < (square original of)ω. Under this reinterpretation, we prove the Generalized Continuum Hypothesis.

Original languageEnglish
Pages (from-to)285-321
Number of pages37
JournalIsrael Journal of Mathematics
Volume116
DOIs
StatePublished - 2000

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