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

• Autorzy: Chris Miller , Patrick Speissegger
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03C99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 162
• Numer: 3
• Strony: 193-208

Daty

wydano

1999

otrzymano

1998-03-23

poprawiono

1999-07-22

Twórcy

autor

Chris Miller

• The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
• Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, OH 43210, U.S.A.

autor

Patrick Speissegger

• Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, U.S.A.
• Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, OH 43210, U.S.A.

Bibliografia

• [CP] Z. Chatzidakis and A. Pillay, Generic structures and simple theories, Ann. Pure Appl. Logic 95 (1998), 71-92.
• [D1] L. van den Dries, The field of reals with a predicate for the powers of two, Manuscripta Math. 54 (1985), 187-195.
• [D2] L. van den Dries, o-Minimal structures, in: Logic: From Foundations to Applications, Oxford Sci. Publ., Oxford Univ. Press, New York, 1996, 137-185.
• [D3] L. van den Dries, Dense pairs of o-minimal structures, Fund. Math. 157 (1998), 61-78.
• [DM] L. van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J. 84 (1996), 497-540.