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Keywords:
boolean algebra; partial order; CCC
boolean algebra; partial order; CCC
Summary:
We partially strengthen a result of Shelah from [Sh] by proving that if $\kappa =\kappa ^{\omega }$ and $P$ is a CCC partial order with e.g. $|P|\leq \kappa ^{+\omega }$ (the $\omega ^{\text{th}}$ successor of $\kappa $) and $|P|\leq 2^{\kappa }$ then $P$ is $\kappa $-linked.
References:
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[HJSh] Hajnal A., Juhász I., Shelah S.: Splitting strongly almost disjoint families. Transactions of the AMS 295 (1986), 369-387. MR 0831204
[HJSz] Hajnal A., Juhász I., Szentmiklóssy Z.: Compact CCC spaces of prescribed density. in: Combinatorics, P. Erdös is 80, Bolyai Soc. Math. Studies, Keszthely, 1993, pp.239-252. MR 1249715
[K] Kunen K.: Set Theory. North Holland, Amsterdam, 1979. MR 0756630 | Zbl 0960.03033
[S] Shelah S.: Remarks on Boolean algebras. Algebra Universalis 11 (1980), 77-89. MR 0593014 | Zbl 0451.06015
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