- Citations (16)
- Cited In (0)

- [Show abstract] [Hide abstract]

**ABSTRACT:**Let ℳ=(M,<) be a linearly ordered structure. ℳ is o-minimal if every definable subset of M is a finite union of intervals. Classical examples are ordered divisible abelian groups and real closed fields. We prove a trichotomy theorem for the structure that an arbitrary o-minimal ℳ can induce on a neighborhood of any a in M. Roughly said, either (i) a is trivial (technical term), or (ii) a has a convex neighborhood on which ℳ induces the structure of an ordered vector space, or (iii) a is contained in an open interval on which ℳ induces the structure of an expansion of a real closed field. The proof uses “geometric calculus” which allows to recover a differentiable structure by purely geometric methods.Proceedings of the London Mathematical Society 01/1998; 77(3):481-523. · 1.15 Impact Factor -
##### Conference Paper: "Geometrical" stability theory.

Logic Colloquium '85, Orsay, France; 01/1985 -
##### Article: MODEL THEORY OF DIFFERENCE FIELDS

[Show abstract] [Hide abstract]

**ABSTRACT:**A dierence eld is a eld with a distinguished automorphism . This paper studies the model theory of existentially closed dierence elds. We introduce a dimension theory on formulas, and in particular on dierence equa- tions. We show that an arbitrary formula may be reduced into one-dimensional ones, and analyze the possible internal structures on the one-dimensional for- mulas when the characteristic is 0.

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.