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Far East Journal of Mathematical Sciences (FJMS)

equipped with a dense linear ordering < without endpoints is said to be o-minimal (weakly o-minimal) if every definable subset of R is a finite union of intervals (convex sets), respectively. A weakly o-minimal structure

expanding an ordered group

is said to be non-valuational if for every cut

definable in

we have that

L. van den Dries proved that every o-minimal expansion of a real closed field admits a

cell decomposition for each positive integer r. In this paper, we prove the non-valuational weakly o-minimal version of it.

Far East Journal of Mathematical Sciences (FJMS)
Volume 25, Issue 3, Pages 417 - 431 (June 2007)

STRONG CELL DECOMPOSITIONS IN NON-VALUATIONAL WEAKLY O-MINIMAL REAL CLOSED FIELDS
Hiroshi Tanaka (Japan) and Tomohiro Kawakami (Japan)

Abstract:
A structure

equipped with a dense linear ordering < without endpoints is said to be o-minimal (weakly o-minimal) if every definable subset of R is a finite union of intervals (convex sets), respectively. A weakly o-minimal structure

expanding an ordered group

is said to be non-valuational if for every cut

definable in

we have that

L. van den Dries proved that every o-minimal expansion of a real closed field admits a

cell decomposition for each positive integer r. In this paper, we prove the non-valuational weakly o-minimal version of it.

Keywords and phrases: weakly o-minimal,

strong cells,

strong cell decompositions, real closed fields.

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