## Homology groups of types in model theory and the computation of $$H_2(p)$$.(English)Zbl 1349.03031

Summary: We present definitions of homology groups $$H_n(p)$$, $$n \geq 0$$, associated to a complete type $$p$$. We show that if the generalized amalgamation properties hold, then the homology groups are trivial. We compute the group $$H_2(p)$$ for strong types in stable theories and show that any profinite abelian group can occur as the group $$H_2(p)$$.

### MSC:

 03C45 Classification theory, stability, and related concepts in model theory 03C60 Model-theoretic algebra 20K40 Homological and categorical methods for abelian groups
Full Text: