Automorphisms of $\mathcal P(\omega)/\mbox{fin}$ and large continuum

TL;DR

This paper demonstrates that it is consistent for the continuum to be larger than  while all automorphisms of the quotient algebra ()/fin are trivial, addressing a longstanding question in set theory.

Contribution

It establishes the consistency of having a large continuum with only trivial automorphisms of ()/fin, advancing understanding of automorphism structures under set-theoretic assumptions.

Findings

Proves the consistency of > with all automorphisms trivial

Shows that nontrivial automorphisms can be eliminated in models with large continuum

Provides new insights into the automorphism problem in Boolean algebras

Abstract

We prove that it is consistent with $\mathfrak c>\aleph_2$ that all automorphisms of $\mathcal P(\omega)/\mbox{fin}$ are trivial.