Expansions of the real line by open sets: o-minimality and open cores
Fundamenta Mathematicae, Tome 162 (1999) no. 3, pp. 193-208
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The open core of a structure ℜ := (ℝ,,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core of ℜ is o-minimal.
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author = {Chris Miller and Patrick Speissegger},
title = {Expansions of the real line by open sets: o-minimality and open cores},
journal = {Fundamenta Mathematicae},
pages = {193--208},
publisher = {mathdoc},
volume = {162},
number = {3},
year = {1999},
doi = {10.4064/fm-162-3-193-208},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-162-3-193-208/}
}
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Chris Miller; Patrick Speissegger. Expansions of the real line by open sets: o-minimality and open cores. Fundamenta Mathematicae, Tome 162 (1999) no. 3, pp. 193-208. doi: 10.4064/fm-162-3-193-208
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