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Strong Limit Cardinal

A strong limit cardinal is an infinite cardinal number kappa such that

2^lambda<kappa,

for every cardinal number lambda<kappa. Equivalently, if a set has a cardinal number less than kappa, then its power set also has a cardinal number less than kappa. Every strong limit cardinal is a limit cardinal, but the converse need not hold.

See also

Cardinal Number, Limit Cardinal, Power Set

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References

Jech, T. Set Theory, 3rd millennium ed. Berlin, Germany: Springer-Verlag, 2003.

Cite this as:

Weisstein, Eric W. "Strong Limit Cardinal." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StrongLimitCardinal.html

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