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So does this article prove that two uncountable infinities are equal? Can you tell us precisely what two entities have been proven equal in this article? I und

So does this article prove that two uncountable infinities are equal? Can you tell us precisely what two entities have been proven equal in this article? I understand aleph-0, aleph-1 and 2^aleph-0 and I also understand that if continuum hypothesis is true, then aleph-1 = 2^aleph-0. Is this what these mathematicians have proven, or have they proven something else?

bjl 9y ago
The paper proves that the smallest cardinality of a set of integers (such that every finite subset has infinite intersections and has no almost-intersections) is equal to the smallest cardinality of a tower.