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On transfinite splittings of infinite sets. (English) Zbl 0748.05009

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
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