Some results on the $\ddot{I}€$-weight of countable Fréchet-Urysohn spaces

Abstract

The $\ddot{I}€$-weight spectrum for countable regular Fréchet-Urysohn spaces is the set of uncountable cardinals that are equal to the $\ddot{I}€$-weight for some such space. We determine this $\ddot{I}€$-weight spectrum in the standard Miller rational perfect set model and in the Random real model.