Logic Seminar
David Lippel
Norte Dame University
Positive elimination in valued fields.
Abstract: A "positive elimination theorem" is a statement that certain positive
existential formulas are equivalent to positive quantifier-free
formulas. Here is a classical example. Let X be a Zariski-closed subset
of a complex projective space. Concretely, X is the solution set of a
system of homogeneous polynomial equations; thus, X has a positive
quantifier-free definition in the language of rings. Let Y be a
coordinate projection of X, so Y has a positive existential definition.
Classical elimination theory says that Y is Zariski-closed, i.e. Y is
actually defined by a positive quantifier-free formula.
Prestel has proved some positive elimination results for valued fields,
working in a one-sorted language. I will discuss some generalizations to
two-sorted languages; these can be used to re-prove some basic facts in
tropical geometry. This is joint work with Matthias Aschenbrenner and
Sergei Starchenko.
tea at 4, talk shortly thereafter.
Monday April 14, 2008 at 4:00 PM in SEO 427