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Elementary equivalence of lattices of open sets definable in o-minimal expansions of fields
 

Summary: Elementary equivalence of lattices of open sets
definable in o-minimal expansions of fields
V. Astier
1 Introduction
It is well-known 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to R, the situation becomes more complicated: Unpublished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

  

Source: Astier, Vincent - Department of Mathematics, University College Dublin

 

Collections: Mathematics