The analysis uncovers insights into uncountable branches in uncountable trees, suggesting implications for cardinality in set theory.
Given an uncountable tree with countable levels, is there always an uncountable branch? To formulate this question properly takes some work, which we will do, and we will then see that the answer is quite subtle. Along the way, we will see singular, regular, inaccessible, measurable, and supercompact cardinals, and have a glimpse of how forcing works.
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Dima Sinapova (2025) studied this question.
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