 
Summary: Elementary equivalence of lattices of open sets
definable in ominimal expansions of fields
V. Astier
1 Introduction
It is wellknown that any two real closed fields R and S are elementarily
equivalent. We can then consider some simple constructions of new structures
out of real closed fields, and try to determine if these constructions, when
applied to R and S, give elementarily equivalent structures. We can for
instance consider def(Rn
, R), the ring of definable functions from Rn
to R,
and we obtain without difficulty that the rings def(Rn
, R) and def(Sn
, S) are
elementarily equivalent ([1]).
However, if we consider cdef(Rn
, R), the ring of continuous definable func
tions from Rn
to R, the situation becomes more complicated: Unpublished
results of M. Tressl show that, for n > 1, cdef(Rn
