generalized continuum hypothesis

The generalized continuum hypothesis states that for any infiniteMathworldPlanetmath cardinal λ there is no cardinal κ such that λ<κ<2λ.

An equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath condition is that α+1=2α for every ordinalMathworldPlanetmathPlanetmath α. Another equivalent condition is that α=α for every ordinal α.

Like the continuum hypothesisMathworldPlanetmath, the generalized continuum hypothesis is known to be independent of the axioms of ZFC.

Title generalized continuum hypothesis
Canonical name GeneralizedContinuumHypothesis
Date of creation 2013-03-22 12:05:31
Last modified on 2013-03-22 12:05:31
Owner yark (2760)
Last modified by yark (2760)
Numerical id 15
Author yark (2760)
Entry type Axiom
Classification msc 03E50
Synonym generalised continuum hypothesis
Synonym GCH
Related topic AlephNumbers
Related topic BethNumbers
Related topic ContinuumHypothesis
Related topic Cardinality
Related topic CardinalExponentiationUnderGCH
Related topic ZermeloFraenkelAxioms