O-minimal fields with standard part map

• Autorzy: Jana Maříková
• Języki publikacji: EN

Abstrakty

EN

Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V → k. Let $k_{ind}$ be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in $k_{ind}$ and conditions on (R,V) which imply o-minimality of $k_{ind}$. We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in $k_{ind}$ are exactly the standard parts of the sets definable in (R,V).

Kategorie tematyczne

• 03C64: Model theory of ordered structures; o-minimality

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 209
• Numer: 2
• Strony: 115-132

Daty

wydano

2010

Twórcy

autor

Jana Maříková

• Department of Mathematics, WIU, 476 Morgan Hall, 1 University Circle, Macomb, IL 61455, U.S.A.

Identyfikatory

DOI

10.4064/fm209-2-2