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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.12659 |
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| _version_ | 1866918152101691392 |
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| author | Grätzer, George |
| author_facet | Grätzer, George |
| contents | For the finite ordered sets $A, D$, write $A^D$ for the ordered set of isotone maps $D \to A$ 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 $A^{(A^A)}$ and $(A^A)^A$. Our main theorem shows that the structure of $A^D$ determines~$A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on the ordered set $A^A$ II. Higher Exponentials Grätzer, George Combinatorics Rings and Algebras 06 For the finite ordered sets $A, D$, write $A^D$ for the ordered set of isotone maps $D \to A$ 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 $A^{(A^A)}$ and $(A^A)^A$. Our main theorem shows that the structure of $A^D$ determines~$A$. |
| title | Notes on the ordered set $A^A$ II. Higher Exponentials |
| topic | Combinatorics Rings and Algebras 06 |
| url | https://arxiv.org/abs/2509.12659 |