Submission date: 29 March 2010.

Abstract:

We show that the generic automorphism is axiomatisable in the green field of Poizat (once Morleyised) as well as in the bad fields which are obtained by collapsing this green field to finite Morley rank. As a corollary, we obtain âbad pseudofinite fieldsâ in characteristic 0.
In both cases, we give geometric axioms. In fact, a general framework is presented allowing this kind of axiomatisation. We deduce from various constructibility results for algebraic varieties in characteristic 0 that the green and bad fields fall into this framework. Finally, we give similar results for other theories obtained by Hrushovski amalgamation, e.g. the free fusion of two strongly minimal theories having the definable multiplicity property.A(

Mathematics Subject Classification: Primary: 03C45; Secondary: 03C35, 03C60, 03C65.

Keywords and phrases: Model Theory, Bad Field, Generic Automorphism, Hrushovski Construction.

Full text arXiv: pdf, ps.