, Volume 116, Issue 1, pp 285321
First online:
The generalized continuum hypothesis revisited
 Saharon ShelahAffiliated withInstitute of Mathematics, The Hebrew University of JerusalemDepartment of Mathematics, Rutgers University Email author
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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 enoughK < ℶ_{ w }. Under this reinterpretation, we prove the Generalized Continuum Hypothesis.
 Title
 The generalized continuum hypothesis revisited
 Journal

Israel Journal of Mathematics
Volume 116, Issue 1 , pp 285321
 Cover Date
 200012
 DOI
 10.1007/BF02773223
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
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 Authors

 Saharon Shelah ^{(1)} ^{(2)}
 Author Affiliations

 1. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel
 2. Department of Mathematics, Rutgers University, 08854, New Brunswick, NJ, USA