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One-dimensional groups definable in o-minimal structures

✍ Scribed by Adam W. Strzebonski

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 707 KB
Volume: 96
Category: Article
ISSN: 0022-4049
DOI: 10.1016/0022-4049(94)90128-7

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📜 SIMILAR VOLUMES

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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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## 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

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## Abstract It is shown that if (__M__, <, ⃛) is an o‐minimal structure such that (__M__, <) is a dense total order and ≾ is a parameter‐definable partial order on __M__, then ≾ has an extension to a definable total order.