Definable linear orders definably embed into lexicographic orders in o-minimal structures
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- by Janak Ramakrishnan PDF
- Proc. Amer. Math. Soc. 141 (2013), 1809-1819
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.References
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Additional Information
- Janak Ramakrishnan
- Affiliation: CMAF, University of Lisbon, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
- Email: janak@janak.org
- 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
- © Copyright 2012 Janak Ramakrishnan
- Journal: Proc. Amer. Math. Soc. 141 (2013), 1809-1819
- MSC (2010): Primary 03C64; Secondary 06A05
- DOI: https://doi.org/10.1090/S0002-9939-2012-11424-8
- MathSciNet review: 3020867