Thursday, September 12, 2024 - 11:30

625 Thackeray Hall

### Abstract or Additional Information

I'm going to talk about an old question of van Douwen: Are the shift map and its inverse conjugate in the automorphism group of P(ω)/fin? By the late 1980's, van Douwen and Shelah proved that it is consistent they are not conjugate. Specifically, any automorphism witnessing their conjugacy would need to be nontrivial (van Douwen), but it is consistent that all automorphisms are trivial (Shelah). In this talk I'm going to discuss the complementary result: it is consistent that the shift map and its inverse are conjugate and, in fact, it follows from CH.