Dividing and chain conditions (Q1423639)

The author gives a chain condition for dividing in an arbitrary theory. A shorter proof of a chain condition result of \textit{S. Shelah} [Ann.\ Math.\ Logic 19, 177--203 (1980; Zbl 0489.03008)] for simple theories and a shorter proof of a result of \textit{O. Lessmann} [Colloq. Math. 83, No. 2, 201--208 (2000; Zbl 0961.03029)] on the maximal number of pairwise inconsistent partial types in a simple theory are given. Now, the proofs rely on the Erdös-Rado Theorem instead of Fodor's Lemma and stationary sets as before.