Definable linear orders definably embed into lexicographic orders in o-minimal structures
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 (Rn+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.
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