Timeline for Two versions of "absolutely ccc"

8 events

when toggle format	what		by	license	comment
Jun 9, 2013 at 21:34	answer	added	Monroe Eskew		timeline score: 6
Jun 8, 2013 at 6:45	comment	added	Monroe Eskew		How do you prove that the Knaster property is indestructible?
Mar 24, 2012 at 23:08	comment	added	saf		Thanks, Arthur. I stand corrected! (indeed, if there is a non-Knaster ($ccc$) poset, then there is one of size $\aleph_1$.) The fact I had in mind is that any $ccc$ poset of size $<\mathfrak{m}$ is $\sigma$- centered.
Mar 24, 2012 at 8:01	comment	added	user642796		@saf: See e.g., Jech (3rd ed.), Theorem 16.21, p.277. The proof actually gives the slightly stronger result that MA$_{\aleph_1} $implies that all ccc posets have precalibre $\aleph_1$.
Mar 24, 2012 at 0:59	comment	added	saf		Be careful! Martin's Axiom implies that any $ccc$ poset of size less than the continuum is Knaster.
Mar 23, 2012 at 18:23	answer	added	Goldstern		timeline score: 1
Mar 23, 2012 at 17:32	comment	added	Joel David Hamkins		One also sometimes sees a weaker notion, asserting only that $\cal P$ remains ccc after forcing with $\cal P$ itself. This is equivalent to saying that ${\cal P}\times{\cal P}$ is ccc.
Mar 23, 2012 at 17:04	history	asked	user642796	CC BY-SA 3.0