Con(u>i)

We prove here the consistency of u>i where: u=Min{|X|:X{subset double equals}P(ω) generates a non-principle ultrafilter}, i=Min{|A|:A is a maximal independent family of subsets of ω} In this we continue Goldstern and Shelah [G1Sh388] where Con(r>u) was proved using a similar but different forcing. We were motivated by Vaughan [V] (which consists of a survey and a list of open problems). For more information on the subject see [V] and [G1Sh388].