PreprintCC BY 4.0arXiv
Definably isometric cuboids over Hensel minimal fields
Abstract
We show that, over a valued field K with $1$-h-minimal theory Th(K), two Cartesian products of balls must be equal up to translation and coordinate permutation in order for there to exist a definable surjective isometry between them. For this purpose, we introduce a notion of relative dimension for cuboids in Kn that is computed combinatorially and relates to the notion of dimension for definable sets in Hensel minimal theories when K has infinite residue field.
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BibTeX
@misc{fortmann2026definably,
title = {{Definably isometric cuboids over Hensel minimal fields}},
author = {Marcelo Fortmann},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06413},
eprint = {2611.06413},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06413},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Definably isometric cuboids over Hensel minimal fields
AU - Marcelo Fortmann
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06413
UR - https://arxiv.org/abs/2611.06413
AB - We show that, over a valued field K with $1$-h-minimal theory Th(K), two Cartesian products of balls must be equal up to translation and coordinate permutation in order for there to exist a definable surjective isometry between them. For this purpose, we introduce a notion of relative dimension for cuboids in K^n that is computed combinatorially and relates to the notion of dimension for definable sets in Hensel minimal theories when K has infinite residue field.
ER -