Projective Determinacy from long Chang's Conjecture

Abstract

Consider the property $({\aleph }_{\omega +1},{\aleph }_{\omega +2},\dots )\twoheadrightarrow ({\aleph }_1,{\aleph }_2,\dots )$. Here we will show that this property with the addition of the General Continuum Hypothesis implies projective determinacy. Of particular interest here is the use of a variant covering argument to prove limited instances of mouse reflection. We believe that this approach could find use for other forms of Chang's Conjecture as well.