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Reducts of some structures over the reals

Published online by Cambridge University Press:  12 March 2014

Ya′acov Peterzil
Ya′acov Peterzil*
Affiliation:
Department of Mathematics, McGill University, Montréal, Québec H3A 2K6, Canada Institute of Mathematics, 24–29 St. Giles, Oxford, OXI 3LB, England, E-mail: [email protected]
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Abstract

We consider reducts of the structure ℛ = 〈ℝ, +, ·, <〉 and other real closed fields. We compete the proof that there exists a unique reduct between 〈ℝ, +, <,λa〉a ∈ 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 〈ℝ, ·, <〉 and ℛ and for general real closed fields.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 3 , September 1993 , pp. 955 - 966
Copyright
Copyright © Association for Symbolic Logic 1993

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