I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018.
Title: In praise of C-sequences.
Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that any fat set may be split into two? Shelah and Ben-David proved that, assuming GCH, if the successor of a singular cardinal carries a special Aronszajn tree, then it also carries a distributive Aronszajn tree. What happens if we relax “special Aronszajn” to just “Aronszajn”? Shelah proved that the product of two $\omega_2$-cc posets need not be $\omega_2$-cc. How about the product of countably many $\omega_2$-Knaster posets?
It turns out that a common strategy for answering all of the above questions is the study of C-sequences. In this series of lectures, we shall provide a toolbox for constructing C-sequences, and unveil a spectrum of applications.
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