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Results tagged with infinite-combinatorics
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user 114946
Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
3
votes
1
answer
206
views
Does the Hawaiian Earring Group embed into the permutation group of $\mathbb N$?
Recall that the Hawaiian earring group, $\mathbb G$, is the fundamental group of the Hawaiian Earing using the point at the origin. It can be understood more combinatorially as a subgroup of the inver …
- 1,882
8
votes
1
answer
228
views
Aronszajn Trees when AC fails
This question may be easy and indicative of my ignorance about the failure of the axiom of choice. If so, I apologize. Below assume $\mathsf{DC}$ but not $\mathsf{AC}$. Suppose we have a partial order …
- 1,882
11
votes
1
answer
478
views
Ways to add Aronszajn trees which are neither Souslin nor special
By an Aronszajn tree, I mean a tree of height $\omega_1$ with countable levels and no branch. Such a tree is Souslin if it has no uncountable antichains and special if it can be written as the countab …
- 1,882