Definable linear orders definably embed into lexicographic orders in o-minimal structures
Logic
2010-11-09 v5
Abstract
We completely characterize definable linear orders in o-minimal structures expanding groups. For example, let (P,<_p) be a linear order definable in the real field R. Then (P,<_p) embeds definably in (R^{n+1},<_l), where <_l is the lexicographic order and n is the o-minimal dimension of P. This improves a result of Onshuus and Steinhorn in the o-minimal group context.
Keywords
Cite
@article{arxiv.1003.5400,
title = {Definable linear orders definably embed into lexicographic orders in o-minimal structures},
author = {Janak Ramakrishnan},
journal= {arXiv preprint arXiv:1003.5400},
year = {2010}
}
Comments
9 pages (substantial rewrite from previous version)