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Expansions of the real line by open sets: o-minimality and open cores

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Miller C., Speissegger P.

Fundamenta Mathematicae

1999

tom 162

nr 3

193-208

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Miller C.

1 Speissegger P.

1 1999

Wyniki wyszukiwania

Expansions of the real line by open sets: o-minimality and open cores