Editing Zero sharp (section)

==Statements implying existence==

The condition about the existence of a Ramsey cardinal implying that <math>0^\sharp</math> exists can be weakened.  The existence of <math>\omega_1</math>-[[Erdős cardinal]]s implies the existence of <math>0^\sharp</math>. This is close to being best possible, because the existence of <math>0^\sharp</math> implies that in the constructible universe there is an <math>\alpha</math>-Erdős cardinal for all countable <math>\alpha</math>, so such cardinals cannot be used to prove the existence of <math>0^\sharp</math>.

[[Chang's conjecture]] implies the existence of <math>0^\sharp</math>.