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Transseries and polynomially bounded o-minimality

Wednesday 1st June 2005 - 14:00 to 15:00
INI Seminar Room 1

`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].

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons