[EstudiantesMatemática] Conferencia de Raffalli (Cmat) - Hilbert's 17th problem via cut-elimination

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Reenvío.


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Date: Mon, 3 Mar 2014 22:23:18 -0200
From: Walter Ferrer <wrferrer en gmail.com>
Subject: Re: [Todos CMAT] Conferencia de Raffalli (Cmat)

  
Title: Hilbert's 17th problem via cut-elimination

Christophe Raffalli
Univ. de Savoie
Sala de Conferencias del Piso 15
Cmat
Miercoles 5 de marzo, 11horas



 

 Abstract: Hilbert's seventeen problem, solved by Artin, says that
 every positive polynomial can be written as a sum of squares of
 rational fraction. Since Artin, effective proof have been given by
 Lombardi - Roy - Perrucci for the latest one which give a bound to the
 degree as a tower of five exponentials.

 We will see how such a proof can be presented as a result of cut
 elimination, showing that replacing model theory by proof theory is a
 possible method to make a result effective.

 The main contribution of our work is the fact that we implemented the
 procedure and we introduced a notion of PBDD that requires smaller
 degrees, making it possible to extract the wanted equalities yet only for
 the
 simplest positive polynomials (which was not possible before from such an
 effective proof).
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