Nowhere trivial automorphisms of $P(\lambda)/[\lambda]^{<\lambda}$, for $\lambda$ inaccessible

TL;DR

This paper proves that under certain set-theoretic assumptions, the Boolean algebra formed by subsets of an inaccessible cardinal modulo small subsets admits a nowhere trivial automorphism, revealing complex symmetry properties.

Contribution

It establishes the existence of nowhere trivial automorphisms of $ ext{P}( ext{inaccessible} ext{ cardinal})/[ ext{cardinal}]^{< ext{cardinal}}$ under specific conditions, a novel result in set theory.

Findings

Existence of nowhere trivial automorphisms under inaccessibility and continuum assumptions

Automorphisms are non-trivial on large parts of the algebra

Results extend understanding of automorphism structure in large cardinal contexts

Abstract

If $\lambda$ is (strongly) inaccessible and $2^\lambda = \lambda^+$, then there is a nowhere trivial automorphism of the Boolean algebra $\mathcal P(\lambda)/[\lambda]^{<\lambda}$.