Definable linear orders definably embed into lexicographic orders in o-minimal structures

摘要

We classify definable linear orders in o-minimal structures expanding groups. For example, let (P,?) be a linear order definable in the real field. Then (P,?) embeds definably in (?~(n+1),<_(lex)), where <_(lex) 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.