Juris Steprans: Non-trivial automorphisms of $P(\omega_1)/fin$

7 March 2014, 13:30–15:00
Fields institute, Room 210

Speaker:  Juris Steprans

Title:  Non-trivial automorphisms of $P(\omega_1)/fin$

Abstract:
Just as in the case of automorphisms of $P(\omega)/fin$, an automorphism of $P(\omega_1)/fin$ will be called trivial if it is induced by a bijection between cofinite subsets of $\omega_1$. Since a non-trivial automorphism of $P(\omega)/fin$ can easily be extended to a non-trivial automorphism of $P(\omega_1)/fin$ there is little interest examining the existence of non-trivial automorphisms of $P(\omega_1)/fin$ without further restrictions. So, an automorphism of $P(\omega_1)/fin$ will be called really non-trivial if it is non-trivial, yet its restriction to any subalgebra of the form $P(X)/fin$ is trivial when $X$ is countable.
It will be shown to be consistent with set theory that there is a really non-trivial automorphism of $P(\omega_1)/fin$. This is joint work with Assaf Rinot.

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