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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 21 juin 2013, 16h

Lieu : IHP, salle 314

Newton-Puiseux Theorem for convergent generalised power series

Tamara Servi (CMAF Lisbonne)

A generalised power series (in several variables) is a series with real nonnegative exponents whose support is contained in a cartesian product of well-ordered subsets of the real line. Let A be the collection of all convergent generalised power series. I will show that, if f(x_1,...,x_n,y) is in A, then the solutions y=g(x_1,...,x_n) of the equation f=0 can be expressed as terms of the language which has a symbol for every function in A and a symbol for division. The construction of the terms is rather explicit. If instead of solving just one equation one wants to solve a system of equations, then one needs a different argument and the proof I will exhibit is a lot less constructive.


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