REDUCTS OF SOME STRUCTURES OVER THE REALS

We consider reducts of the structure R = [R, +, ., <] and other real c losed fields. We compete the proof that there exists a unique reduct b etween [R, +, <, lambda(a)]a is-an-element-of R and R, and we demonstr ate how to recover the definition of multiplication in more general co ntexts than the semialgebraic one. We then conclude a similar result f or reducts between [R, ., <] and R and for general real closed fields.