In this link, the following list appears:
Some chain conditions [of posets], listed from easiest to satisfy to hardest to satisfy:
- ccc
- powerfully ccc
- productively ccc
- $\sigma$-finite-cc
- $\sigma$-bounded-cc
- $\sigma$-$2$-linked
- $\sigma$-$n$-linked
- $\sigma$-$n$-linked $\forall n$
- $\sigma$-centered
- countable
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)?