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

Author: Janak Ramakrishnan
Journal: Proc. Amer. Math. Soc. 141 (2013), 1809-1819
MSC (2010): Primary 03C64; Secondary 06A05
Published electronically: October 10, 2012
MathSciNet review: 3020867
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Abstract: We classify definable linear orders in o-minimal structures expanding groups. For example, let $ (P,\prec )$ be a linear order definable in the real field. Then $ (P,\prec )$ embeds definably in $ (\mathbb{R}^{n+1},<_{\text {lex}})$, where $ <_{\text {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.

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Additional Information

Janak Ramakrishnan
Affiliation: CMAF, University of Lisbon, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal

Received by editor(s): December 16, 2010
Received by editor(s) in revised form: August 29, 2011
Published electronically: October 10, 2012
Additional Notes: The author was supported by ANR chaire d’excellence junior THEMODMET (ANR-06-CEXC-007)
Communicated by: Julia Knight
Article copyright: © Copyright 2012 Janak Ramakrishnan

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