Reducts of some structures over the reals

Journal of Symbolic Logic 58 (3):955-966 (1993)
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Abstract

We consider reducts of the structure $\mathscr{R} = \langle\mathbb{R}, +, \cdot, <\rangle$ and other real closed fields. We compete the proof that there exists a unique reduct between $\langle\mathbb{R}, +, <, \lambda_a\rangle_{a\in\mathbb{R}}$ and R, and we demonstrate how to recover the definition of multiplication in more general contexts than the semialgebraic one. We then conclude a similar result for reducts between $\langle\mathbb{R}, \cdot, <\rangle$ and R and for general real closed fields

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Structure theorems for o-minimal expansions of groups.Mario J. Edmundo - 2000 - Annals of Pure and Applied Logic 102 (1-2):159-181.
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Non-standard lattices and o-minimal groups.Pantelis E. Eleftheriou - 2013 - Bulletin of Symbolic Logic 19 (1):56-76.

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References found in this work

Tame Topology and O-Minimal Structures.Lou van den Dries - 2000 - Bulletin of Symbolic Logic 6 (2):216-218.

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