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O-minimal fields with standard part map

Jana Maříková (2010)

Fundamenta Mathematicae

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 i n d be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in k i n d and conditions on (R,V) which imply o-minimality of k i n d . 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 i n d are exactly the standard parts of the sets definable in (R,V).

On a decomposition of polynomials in several variables

Andrzej Schinzel (2002)

Journal de théorie des nombres de Bordeaux

One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.

Currently displaying 961 – 980 of 2019