Submission date: 10 November 2015

Abstract:

In this article, we show that the first homology group of strong type H_1(p) is well-defined for any strong type p in any theory, and this group is given by the quotient of automorphism group G of p by the normal subgroup of automorphisms fixing each orbit on p(M) under the action of the derived group G'. We also suggest a candidate of Lascar group localized at p, the quotient of G by the normal subgroup of automrophisms fixing all Lascar equivalence class of arbitrary length of realizations of p, which does not depend on the choice of monster model. Using this Lascar group, we show that there is a canonical epimorphism from this Lascar group to the first homology group for a strong type in an arbitrary theory.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1511.03410: pdf, ps.