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The Journal of Symbolic Logic Volume 00, Number 0, XXX 0000
 

Summary: The Journal of Symbolic Logic
Volume 00, Number 0, XXX 0000
STRONGLY MINIMAL GROUPS IN THE THEORY OF COMPACT
COMPLEX SPACES
MATTHIAS ASCHENBRENNER , RAHIM MOOSA
, AND THOMAS SCANLON
Abstract. We characterise strongly minimal groups interpretable in elementary extensions of compact
complex analytic spaces.
1. Introduction. In [21] Zilber observed that compact complex manifolds may
be naturally regarded as structures of finite Morley rank for which the axioms of
Zariski-type structures hold. As such, the key to a model theoretic structure theory
for sets definable in compact complex manifolds is a description of the interpretable
strongly minimal groups. Pillay and the third author described these groups in [16]
but left open the question of what strongly minimal groups might be definable in
elementary extensions of compact complex manifolds. In this paper, we complete
the classification.
We regard a compact complex manifold M as a structure in the language having
a predicate for each closed analytic subvariety of each cartesian power of M. It is
convenient to consider all compact complex analytic spaces at the same time. To
do so, we form the many sorted structure A having a sort for each (isomorphism

  

Source: Aschenbrenner, Matthias - Department of Mathematics, University of California at Los Angeles

 

Collections: Mathematics