Vorträge im Schwerpunkt Reelle Geometrie und Algebra
Freitag, 26. November 2010, um 14:15 Uhr
in F426
(Oberseminar)
Noa Lavi
(Konstanz)
Stellensätze in
Real closed Valued Fields
Abstract:
A “nichtnegativstellensatz” in real algebraic geometry
is a theorem characterizing algebraically those polynomials admitting
only non-negative values on a given set. An original model theoretic
proof for a nightnegativstellensatz is the generalization of A.
Robinson of Hilbert's Seventeenth Problem (first solved by Artin) to
real closed fields. According to the work of G. Cherlin and M. Dickmann
(using AKE theorems), the theory of real closed valued fields admits
quantifier elimination, which allows model theoretic techniques for
obtaining such results for definable sets of a real closed valued
field. In my talk I will show such, demonstrating the connection
between the order and the valuation.
zuletzt
geändert am 22. November 2010
