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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
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