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

Vincent Astier. "Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields." Fundamenta Mathematicae 220.1 (2013): 7-21. <http://eudml.org/doc/282855>.

@article{VincentAstier2013,
abstract = {We prove that the boolean algebras of sets definable in elementarily equivalent o-minimal expansions of real closed fields are back-and-forth equivalent, and in particular elementarily equivalent, in the language of boolean algebras with new predicates indicating the dimension, Euler characteristic and open sets. We also show that the boolean algebra of semilinear subsets of [0,1]ⁿ definable in an o-minimal expansion of a real closed field is back-and-forth equivalent to the boolean algebra of definable subsets of [0,1]ⁿ definable in the same o-minimal expansion, in the language of boolean algebras with new predicates indicating the dimension, Euler characteristic and open sets, as well as related results.},
author = {Vincent Astier},
journal = {Fundamenta Mathematicae},
keywords = {o-minimal structure; Boolean algebra of definable sets; lattice of open definable sets; semilinear set},
language = {eng},
number = {1},
pages = {7-21},
title = {Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields},
url = {http://eudml.org/doc/282855},
volume = {220},
year = {2013},
}

TY - JOUR
AU - Vincent Astier
TI - Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields
JO - Fundamenta Mathematicae
PY - 2013
VL - 220
IS - 1
SP - 7
EP - 21
AB - We prove that the boolean algebras of sets definable in elementarily equivalent o-minimal expansions of real closed fields are back-and-forth equivalent, and in particular elementarily equivalent, in the language of boolean algebras with new predicates indicating the dimension, Euler characteristic and open sets. We also show that the boolean algebra of semilinear subsets of [0,1]ⁿ definable in an o-minimal expansion of a real closed field is back-and-forth equivalent to the boolean algebra of definable subsets of [0,1]ⁿ definable in the same o-minimal expansion, in the language of boolean algebras with new predicates indicating the dimension, Euler characteristic and open sets, as well as related results.
LA - eng
KW - o-minimal structure; Boolean algebra of definable sets; lattice of open definable sets; semilinear set
UR - http://eudml.org/doc/282855
ER -