Abstract
It is shown that there is no satisfactory first-order characterization of those subsets of ω 2 that have closed unbounded subsets in ω 1, ω 2 and GCH preserving outer models. These “anticharacterization” results generalize to subsets of successors of uncountable regular cardinals. Similar results are proved for trees of height and cardinality κ + and for partitions of [ κ +] 2, when κ is an infinite cardinal.
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