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.