On the structure of Borel ideals in-between the ideals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">ED</mml:mi></mml:math> and Fin ⊗ Fin in the Katětov order

For a family F⊆ωω we define the ideal I(F) on ω×ω to be generated by family{A⊆ω×ω:∃f∈F∀∞n(|{k:(n,k)∈A}|≤f(n))}. Using ideals of form I(F), show that structure Borel in-between two well known idealsED={A⊆ω×ω:∃m∀∞n(|{k:(n,k)∈A}|<m))} andFin⊗Fin={A⊆ω×ω:∀∞n(|{k:(n,k)∈A}|<ℵ0))} in Katětov order is fairly complicated. Namely, there copy P(ω)/Fin ED and Fin⊗Fin, consequently are increasing decreasing chains length b antichains size c.