Uniform local weak o-minimality and $*$-local weak o-minimality
Logic
2024-05-13 v1
Abstract
We propose the notions of uniform local weak o-minimality and -local weak o-minimality. Local monotonicity theorems hold in definably complete locally o-minimal structures and uniformly locally o-minimal structures of the second kind. In this paper, we demonstrate new local monotonicity theorems for uniformly locally weakly o-minimal structures of the second kind and for locally o-minimal structures under the assumption called the univariate -continuity property. We also prove that several formulas for dimension of definable sets which hold in definably complete locally o-minimal structures also hold in -locally weakly o-minimal structures possessing the univariate -continuity property.
Cite
@article{arxiv.2405.06140,
title = {Uniform local weak o-minimality and $*$-local weak o-minimality},
author = {Masato Fujita},
journal= {arXiv preprint arXiv:2405.06140},
year = {2024}
}