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An Isaac Newton Institute Programme

Model Theory and Applications to Algebra and Analysis

Transseries and polynomially bounded o-minimality

1st June 2005

Author: Ressayre, Jean-Pierre (Paris 7)


`Transseries' is the short name coined by Ecalle for certain generalised power series - here the name is appropriate to denote all such series. The use of transeries allows the study of o-minimal expansions of the reals to rest on fully model theoretic methods. We develop this theme in case the o-minimal expansion of the reals is polynomially bounded and we prove results of quantifier(s) elimination, of axiomatisation, of cell decomposition and relative computability - in the `restricted case' where the primitive functions added to the real field are C^\infty with arguments ranging over [0,1].