Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 959

Preprint Number 959

Previous Next Preprint server

959. Jan Dobrowolski, Byunghan Kim, and Junguk Lee
The Lascar groups and the 1st homology groups in model theory

Submission date: 10 November 2015


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.

Last updated: November 25 2015 16:09 Please send your corrections to: