Easton's Theorem

If G is a function whose domain and range consist of ordinals and (1) G is non-decreasing, and (2) the cofinality of

\aleph_{G(\alpha)}

is greater than

\aleph_{\alpha}

which is regular, for each α in the domain of G, then forcing can create a model with

2^{\aleph_{\alpha}} = \aleph_{G(\alpha)}

.

SEE ALSO

REFERENCES

Ulrich Felgner,''Models of ZF-Set Theory'',1971,''Lecture Notes in Mathematics'',Springer-Verlag.

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