Notes on the ordered set A^A II. Higher Exponentials

2025/09/16 by George Grätzer, Grätzer, George
Mathematics · #06 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Mathematics and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2509.12659

openalex publication_date 2025/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the finite ordered sets A, D, write A^D for the ordered set of isotone maps D → A with the pointwise order. It was proved in earlier work that the order structure of A^A determines~A up to isomorphism. In this note we extend the result to higher function ordered sets such as A^(AA) and (A^A)^A. Our main theorem shows that the structure of A^D determines~A.

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