Notes on the ordered set $A^A$. Part III. Exponent-cancellations (2509.19221v1)

Published 23 Sep 2025 in math.RA

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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G. Grätzer

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Notes on the ordered set $A^A$. Part III. Exponent-cancellations (3 likes, 0 questions)