ideal $\check I(\lambda)$: the definition is missing

Question

Here on the page 15 in the definition 1.14 is $\check I[\lambda]$ defined but $\check I(\lambda)$ ideal not. Does someone know what is this round brackets notation?

EDIT BTW, on the page 9 there in the same paper, 0.5(3) in the proof of claim 0.14(1) refers to unknown reference. What is the correct place to look at?

Answer 1

It looks to me like $\check I(\lambda)$ is simply a typo of $\check I[\lambda]$, and the complicated definition of "witnesses for $S\in \check I[\lambda]$" was just deferred momentarily from item 1) to item 2) in the enumerated list.