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Results tagged with infinite-combinatorics
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user 22840
Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
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 …
- 4,713
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 …
- 503