In Set Theory - on the structure of the Real Line by Bartoszyński & Judah, a forcing notion $\bf U$ is mentioned on page 339, allegedly corresponding to $\rm{cof}(\cal N)$ as it has several properties allowing it to increase this cardinal without increasing $\rm{cof}(\cal M)$ and $\rm{non}(\cal N)$:
- it is $\omega^\omega$-bounding,
- it preserves both $\sqsubseteq^\rm{Cohen}$ and $\sqsubseteq^\rm{random}$, and
- it does not have the Sacks property
However, they conclude the paragraph immediately after with:
"We will not present the definition of $\bf U$ here since it is quite complicated. The model for which we would use $\bf U$ can be constructed in a much simpler way."
Unfortunately, it seems that the book does not mention any reference to the origin of this forcing notion, or at least not that I could find.
What is this forcing notion $\bf U$?
