Abian, Alexander; Amin, Wael A. On transfinite splittings of infinite sets. (English) Zbl 0748.05009 Rend. Ist. Mat. Univ. Trieste 21, No. 1, 122-127 (1989). Summary: We prove below a rather basic theorem concerning the iterative splitting of a nonempty proper subset of a set (specifically, an infinite cardinal number) into at most two nonempty disjoint subsets. Based on this, the existence of trees with large cardinal heights having some nontrivial properties can be established. MSC: 05A17 Combinatorial aspects of partitions of integers 05C05 Trees 03E10 Ordinal and cardinal numbers Keywords:transfinite splitting; infinite sets PDFBibTeX XMLCite \textit{A. Abian} and \textit{W. A. Amin}, Rend. Ist. Mat. Univ. Trieste 21, No. 1, 122--127 (1989; Zbl 0748.05009)