Comparing Fréchet-Urysohn filters with two pre-orders

A filter F on ω is called Fréchet-Urysohn if the space with only one non-isolated point ω∪{F} is a Fréchet-Urysohn space, where the neighborhoods of the non-isolated point are determined by the elements of F. In this paper, we distinguish some Fréchet-Urysohn filters by using two pre-orderings of filters: One is the Rudin-Keisler pre-order and the other one was introduced by Todorčević-Uzcátegui in [11]. We mainly construct an RK-chain of size c+ which is RK-above of every FU-filter. Also, we show that there is an infinite RK-antichain of FU-filters.