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Compact domination for groups definable in linear o-minimal structures

✍ Scribed by Pantelis E. Eleftheriou

Publisher: Springer
Year: 2009
Tongue: English
Weight: 263 KB
Volume: 48
Category: Article
ISSN: 0933-5846
DOI: 10.1007/s00153-009-0139-1

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We study subgroups G of GL n, R definable in o-minimal expansions M s Ž . Ž. R, q, и , . . . of a real closed field R. We prove several results such as: a G can be defined using just the field structure on R together with, if necessary, power Ž . functions, or an exponential function definable in M.

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Definable group extensions in semi-bounded o-minimal structures

✍ Mário J. Edmundo; Pantelis E. Eleftheriou 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 109 KB

## Abstract In this note we show: Let __R__ = 〈__R__, <, +, 0, …〉 be a semi‐bounded (respectively, linear) o‐minimal expansion of an ordered group, and __G__ a group definable in __R__ of linear dimension __m__ ([2]). Then __G__ is a definable extension of a bounded (respectively, definably compact