Geodesic
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.
DOI : 10.4064/fm-162-3-193-208

Chris Miller 1 ; Patrick Speissegger 1

1 
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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. http://geodesic.mathdoc.fr/articles/10.4064/fm-162-3-193-208/

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