cardinal exponentiation under GCH

Many results about cardinal exponentiationMathworldPlanetmath can neither be proved nor disproved in ZFC. If, however, we allow ourselves to use GCH in addition to ZFC, then we have the following theorem, which gives an essentially completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmath description of the way cardinal exponentiation involving infiniteMathworldPlanetmath cardinals works.


Assume the Generalized Continuum Hypothesis holds. Let κ and λ be cardinals, at least one of which is infinite, and such that κ>0 and λ>1. Then


Here, cf(λ) is the cofinality of λ, and λ+ is the cardinal successor of λ.

Title cardinal exponentiation under GCH
Canonical name CardinalExponentiationUnderGCH
Date of creation 2013-03-22 14:54:04
Last modified on 2013-03-22 14:54:04
Owner yark (2760)
Last modified by yark (2760)
Numerical id 9
Author yark (2760)
Entry type Theorem
Classification msc 03E10
Related topic CardinalArithmetic
Related topic GeneralizedContinuumHypothesis