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 language | English |
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Pages (from-to) | 285-321 |
Number of pages | 37 |
Journal | Israel Journal of Mathematics |
Volume | 116 |
DOIs | |
State | Published - 2000 |