In 1972, Bjarni Jónsson defined a combinatorial property that is related to the Ramsey property, and recently Jackson showed that, in a canonical model of the axiom of determinacy, all uncountable cardinals have this property. In that paper, he asked whether or not this property was true for non-cardinal sets in this model. Using the canonization result that we proved last time, we will prove that the real numbers have this property in that model.