In 1956 W. Rudin proved that the Continuum Hypothesis (CH) implies that the \v Cech--Stone remainder of $ N$ (with the discrete topology), $\beta N\setminus N$, has $2^{2^{\aleph_0}$ homeomorphisms. In 1979, Shelah described a forcing extension of the universe in which every autohomeomorphism of $\beta N\setminus N$ is the restriction of a continuous map of $\beta N$ into itself. Since there are only $2^{\aleph_0}$ such maps, the conclusion contradicts Rudin's. Rudin's result is, by today's standards, trivial: By the Stone Duality, autohomeomorphisms of $\beta N\setminus N$ correspond to automorphisms of the Boolean algebra $P( N)/$Fin. This algebra is countably saturated hence CH implies that it is fully saturated. A standard back-and-forth argument produces a complete binary tree of height $\aleph_1=2^{\aleph_0}$ whose branches are distinct automorphisms. The fact that the theory of atomless Boolean algebras admits elimination of quantifiers is not even used in this argument. On the other hand, Shelah's result is, unlike most of the 1970s memorabilia, still as formidable as when it appeared. Extensions of Shelah's argument (nowadays facilitated by Forcing Axioms) show that this rigidity of $P( N)/$Fin is shared by other similar quotient structures, and that is what this survey is about.
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