PreprintCC BY 4.0arXiv
A minimal type of Morley rank ω in a partial differential field
Abstract
We consider the Kolchin-generic complete $1$-type of the inviscid Burgers equation Dx=x∂ x in a differentially closed field of characteristic zero with two commuting derivations. We prove that this type has Lascar rank $1$ and Morley rank ω.
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BibTeX
@misc{kowalski2026minimal,
title = {{A minimal type of Morley rank $ω$ in a partial differential field}},
author = {Piotr Kowalski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18730},
eprint = {2609.18730},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18730},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A minimal type of Morley rank ω in a partial differential field
AU - Piotr Kowalski
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18730
UR - https://arxiv.org/abs/2609.18730
AB - We consider the Kolchin-generic complete $1$-type of the inviscid Burgers equation Dx=x∂ x in a differentially closed field of characteristic zero with two commuting derivations. We prove that this type has Lascar rank $1$ and Morley rank ω.
ER -