On automorphism groups of metric reduced products of symmetric groups

TL;DR

This paper investigates the structure of automorphism groups of metric reduced products of symmetric groups under certain set-theoretic axioms, revealing insights into their isomorphisms and symmetries.

Contribution

It provides new results on the automorphism groups of metric reduced products of symmetric groups assuming OCA and Martin's axiom, advancing understanding of their algebraic and metric properties.

Findings

Characterizes isomorphisms between such products under set-theoretic assumptions

Establishes conditions for automorphisms in the metric setting

Links set theory axioms with algebraic structure of symmetric groups

Abstract

We study isomorphisms between metric reduced products of symmetric groups with the normalized Hamming metric assuming the open coloring axiom $\mathsf{OCA}$ and Martin's axiom for $\sigma$-linked posets.