# Set theory – Existence of a bijective function that maps the subset tensor product of a selective ultrafilter in the ultrafilter

In the answer to this question, Andreas Blass had shown that for any selective ultrafilter $$scr {U}$$ sure $$omega$$ and for any free subfilter $$scr {F} subset {U}$$ does not exist bijection $$varphi: omega ^ 2 to omega$$ such as $$varphi ( scr {F} otimes scr {F}) subset scr {U}$$. I'm trying to weaken the conditions.

Question: Is there a pair of subassemblies $$scr {A}, scr {B}$$ selective ultrafilter $$scr {U}$$ sure $$omega$$ and a bijection $$varphi: omega ^ 2 to omega$$ with the following properties:

1. $$scr {A}$$ and $$scr {B}$$ have ownership of the finished intersections and $$cap scr {A} = cap scr {B} = varnothing$$
2. $$varphi ( scr {A} otimes scr {B}) subset scr {U}$$ ?