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The Diamond Principle implies the Continuum Hypothesis and the negation of the Suslin Hypothesis.
They satisfy GCH, the diamond principle for all stationary subsets of regular cardinals, the square principle (except at subcompact cardinals), and other principles holding in L.
The constructible universe satisfies the Generalized Continuum Hypothesis, the Diamond Principle, Martin's Axiom and the Kurepa Hypothesis.
In mathematics, and particularly in axiomatic set theory, the diamond principle is a combinatorial principle introduced by Ronald Jensen in that holds in the constructible universe and that implies the continuum hypothesis.
Wörterbuch für Mathematik