Elementary equivalence of lattices of open sets
definable in o-minimal expansions of real closed fields
Fundamenta Mathematicae, Tome 220 (2013) no. 1, pp. 7-21
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
prove boolean algebras sets definable elementarily equivalent o minimal expansions real closed fields back and forth equivalent particular elementarily equivalent language boolean algebras predicates indicating dimension euler characteristic sets boolean algebra semilinear subsets definable o minimal expansion real closed field back and forth equivalent boolean algebra definable subsets definable o minimal expansion language boolean algebras predicates indicating dimension euler characteristic sets related results
Affiliations des auteurs :
Vincent Astier 1
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author = {Vincent Astier},
title = {Elementary equivalence of lattices of open sets
definable in o-minimal expansions of real closed fields},
journal = {Fundamenta Mathematicae},
pages = {7--21},
year = {2013},
volume = {220},
number = {1},
doi = {10.4064/fm220-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm220-1-2/}
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%0 Journal Article %A Vincent Astier %T Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields %J Fundamenta Mathematicae %D 2013 %P 7-21 %V 220 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/fm220-1-2/ %R 10.4064/fm220-1-2 %G en %F 10_4064_fm220_1_2
Vincent Astier. Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields. Fundamenta Mathematicae, Tome 220 (2013) no. 1, pp. 7-21. doi: 10.4064/fm220-1-2
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