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Notes on the ordered set $A^A$. Part III. Exponent-cancellations

Published 23 Sep 2025 in math.RA | (2509.19221v1)

Abstract: We continue the study of exponent-cancellation for finite ordered sets. It is known that $A$ can be reconstructed from $A{A}$, from $(A{A}){A}$, and from $A{A{A}}$. In this note we prove the next result in this hierarchy: the ordered set $(A{A{A}}){A{A{A}}}$ determines $A$ up to isomorphism.

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