Real Algebraic and Analytic Geometry
Submission: 2012, November 5.
We prove that the lattices of open sets definable in a o-minimal expansions fields are back-and-forth equivalent, and in particular elementarily equivalent, in the language of bounded lattices with new predicates indicating the dimension. We also show that the lattice of open semilinear sets definable in a real closed field is back-and-forth equivalent to the latice of open semialgebraic sets definable in the same real closed field, in the language of bounded lattices with new predicates indicating the dimension.
Mathematics Subject Classification (2000): 03C64.
Keywords and Phrases: boolean algebras, open definable sets, open semilinear sets, o-minimal expansions of fields.
Full text, 17p.: dvi 75k, pdf 228k.