%\newcommand{\Om}{\Omega}
%\newcommand{\Omn}{\Omega^{(n)}}
\titleofpresentation{Finite Covers and Congruences}

\presenter{Elisabetta Pastori}

This talk  can be placed  within the area of infinite permutation groups and
their relations with model theory. For brief surveys about this area see for
example \cite{pastoriCa} and \cite{pastoriEMI}.

After giving the definition of finite cover of a structure $W$ (we give it in
terms of the automorphism groups of the structures involved), we show a theorem
 which describes all the possible kernels of finite covers  of a transitive
structure $W$ having all binding groups and fibre groups isomorphic to a simple
non abelian regular group $G$, in terms of the
$\operatorname{Aut}(W)$-congruences on $W$.  
This result has its basis in the article \cite{pastoriEH} . Then we
take in exam the 
case of $W=\Omega^{(n)}$, the set of ordered $n$-tuples with all
distinct entries from 
an infinite set $\Omega$, with
$\operatorname{Aut}(W)=\operatorname{Sym}(\Omega)$ and we show a
result of biinterpretability.


\begin{ourbiblio}{LGO \,}

\bibitem[Ca]{pastoriCa} P. Cameron, \emph{Oligomorphic permutation groups},
London Mathematical Society Lecture Notes Series 152, Cambridge
University Press, Cambridge, 1990.

\bibitem[EH]{pastoriEH} D.M. Evans and E. Hrushovski, \emph{On the automorphism groups
of finite covers},
Annals of Pure and Applied Logic  \textbf{62} (1993),
\mbox{83--112.}

\bibitem [EMI]{pastoriEMI}D. M. Evans, A. A. Ivanov and D. Macpherson, \emph{Finite
covers},
London Mathematical Society Lecture Notes Series 244, Cambridge
University Press, Cambridge, 1977.
\end{ourbiblio}

\presenteraddress{University of Florence, Italy}


\email{pastori@math.unifi.it}

