Remark on a Theorem of Lindström

In a recent paper LindstrSm [I] proves a theorem on finite sets and he also proves a transfinite extension. In this note we only concern ourselves with the transfinite case of Lindstriim’s theorem. He in fact proves the following theorem: Let / Y I = K be an infinite set, and let A,, l<ol< w, , the initial ordinal of cardinality m, m > K, be subsets of Y. Then for every p -=z m there are p disjoint sets of the indices I,, , 1 < y < w?, , so that the p sets