In this link, the following list appears:
Some chain conditions [of posets], listed from easiest to satisfy to hardest to satisfy:
- powerfully ccc
- productively ccc
- $\sigma$-$n$-linked $\forall n$
Is there some reference where these notions are defined and discussed, preferably with separating examples (i.e. showing a poset which is $\sigma$-$n$-linked $\forall n$ but not $\sigma$-centered)?