Abstract

We study the structures $(K \subset K^\mathrm{r})$ , where K is an ordered field and Kr its real closure, in the language of ordered fields with an additional unary predicate for the subfield K. Two such structures $(K \subset K^\mathrm{r})$ and $(L \subset L^\mathrm{r})$ are not necessarily elementary equivalent when K and L are. But with some saturation assumption on K and L, then the two structures become equivalent, and we give a description of the complete theory