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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.

6 votes

Is it known whether every $\omega$-tree with an infinite antichain has an infinite chain in ...

As shown in the OP, if every countable collection of non-empty finite sets has a choice function, then any countable union of finite sets is countable. Suppose that the countable union of finite sets …
Cameron Buie's user avatar
11 votes
1 answer
798 views

Is it known whether every $\omega$-tree with an infinite antichain has an infinite chain in ...

In this paper by Good and Tree, the following result is mentioned without proof as part of Proposition 6.5: Each of the following statements imply those beneath it. The countable union of finite set …
Cameron Buie's user avatar