The Souslin problem
Recall that the real line is that unique separable, dense linear ordering with no endpoints in which every bounded set has a least upper bound.
Around the year of 1920, Souslin asked whether the term *separable* in the above characterization may be weakened to *ccc*. (A linear order is said to be separable if it has a countable dense subset. It is ccc if every pairwise-disjoint family of open intervals is countable.)
Amazingly enough, the resolution of this single problem led to many key discoveries in set theory. Also, consistent counterexamples to this problem play a prominent role in infinite combinatorics.
In this talk, we shall tell the story of the Souslin problem, and report on an advance recently obtained after 40 years of waiting.
תאריך עדכון אחרון : 09/05/2016