Structure theorems for o-minimal expansions of groups

Annals of Pure and Applied Logic 102 (1-2):159-181 (2000)
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Abstract

Let R be an o-minimal expansion of an ordered group R has no poles, R cannot define a real closed field with domain R and order R is eventually linear and every R -definable set is a finite union of cones. As a corollary we get that Th has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R -definable sets and a symbol for each definable endomorphism of the group

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10.1016/s0168-0072(99)00043-3

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Citations of this work

Almost o-minimal structures and X -structures.Masato Fujita - 2022 - Annals of Pure and Applied Logic 173 (9):103144.
Returning to semi-bounded sets.Ya'Acov Peterzil - 2009 - Journal of Symbolic Logic 74 (2):597-617.
Coverings by open cells.Mário J. Edmundo, Pantelis E. Eleftheriou & Luca Prelli - 2014 - Archive for Mathematical Logic 53 (3-4):307-325.

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References found in this work

A structure theorem for semibounded sets in the reals.Ya'acov Peterzil - 1992 - Journal of Symbolic Logic 57 (3):779-794.
Additive reducts of real closed fields.David Marker, Ya'acov Peterzil & Anand Pillay - 1992 - Journal of Symbolic Logic 57 (1):109-117.
Reducts of some structures over the reals.Ya′Acov Peterzil - 1993 - Journal of Symbolic Logic 58 (3):955-966.

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