Submission date: 29 April 2015.

Abstract:

For rosy theories, we give canonical surjective homomorphisms from Lascar groups to the first homology groups of strong types, and we describe its kernel by an invariant equivalence relation. As a consequence, we show that the first homology groups of strong types in rosy theories have the cardinalities of one or at least continuum. We give two examples of rosy theories having non trivial first homology groups of strong types over empty set. In these examples, these two homology groups are exactly isomorphic to their Lascar group over algebraic closures of empty set.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1504.07721: pdf, ps.