Abstract: 

Generalizing classic results of Szmielew for Abelian groups, we give a language for quantifier elimination in any complete theory of a torsion-free Abelian group with a unary predicate for a subgroup. Then we consider the case when there is an additional predicate for a linear ordering, and in some cases we can axiomatize the complete theories, eliminate quantifiers, and compute dp-ranks. This is recent joint work with Alfred Dolich.

Venue:Quan 9 

Zoom: 717 463 6082