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)?

  • 1
    $\begingroup$ Have you tried in the newer Kunen?If I recall correctly most of these notions are there (chap 3/4) $\endgroup$ Jun 7, 2016 at 18:27
  • $\begingroup$ @CarloVonSchnitzel actually no, I'm using the older Kunen. I will check. $\endgroup$
    – Ur Ya'ar
    Jun 7, 2016 at 18:35
  • $\begingroup$ I believe we should have it in the library. The new Kunen. $\endgroup$
    – Asaf Karagila
    Jun 7, 2016 at 18:49
  • 1
    $\begingroup$ @Stefan: A partial order is powerfully ccc if its finite powers are ccc, and productively ccc if its product with each ccc partial order is ccc. $\endgroup$ Jun 7, 2016 at 21:24
  • 2
    $\begingroup$ See matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14114.pdf $\endgroup$
    – hot_queen
    Jun 7, 2016 at 21:35


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