Lascar groups and the first homology groups of strong types in rosy theories

2015/04/29 by Lee, Junguk
#03C45 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1504.07721

Abstract

For a rosy theory, we give a canonical surjective homomorphism from a Lascar group over A=\acl^eq(A) to a first homology group of a strong type over A, 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 2^ℵ₀. We give two examples of rosy theories having non trivial first homology groups of strong types over \acl^eq(∅). In these examples, these two homology groups are exactly isomorphic to their Lascar group over \acl^eq(∅).

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