Reducts of some structures over the reals

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