Type: Article

Are scales Fréchet?

Figueroa-Sierra, Raúl; Guzmán, Osvaldo; Hrušák, Michael; Kwela, Adam;

Abstract:

We continue the study of Dow spaces of a ????-scale, originally introduced by Dow in [14]. We prove that it is consistent that all such spaces are Fréchet, but it is also consistent that none of them is. We use these spaces to exhibit (consistently) a ?1 2 ideal that does not satisfy the Category Dichotomy. Finally, we prove that the Category Dichotomy holds for all co-analytic ideals