Corpus ID: 235458629

Automorphism groups over a hyperimaginary

@inproceedings{Kim2021AutomorphismGO,
  title={Automorphism groups over a hyperimaginary},
  author={Byunghan Kim and Hyo-Tae Lee},
  year={2021}
}
In this paper we study the Lascar group over a hyperimaginary e. We verify that various results about the group over a real set still hold when the set is replaced by e. First of all, there is no written proof in the available literature that the group over e is a topological group. We present an expository style proof of the fact, which even simplifies existing proofs for the real case. We further extend a result that the orbit equivalence relation under a closed subgroup of the Lascar group… Expand

References

SHOWING 1-10 OF 15 REFERENCES
Hyperimaginaries and automorphism groups
TLDR
This paper shows that if T is simple and canonical bases of Lascar strong types exist in Meq then hyperimaginaries can be eliminated in favour of sequences of ordinary imaginaries, and develops a Galois theory of T, making use of the structure of compact groups. Expand
The diameter of a Lascar strong type
We prove that a type-denable Lascar strong type has nite diameter. We also answer some other questions from (1) on Lascar strong types. We give some applications on subgroups of type-denable groups.Expand
The Lascar Group and the Strong Types of Hyperimaginaries
  • Byunghan Kim
  • Mathematics, Computer Science
  • Notre Dame J. Formal Log.
  • 2013
TLDR
The Lascar group is studied in slightly more general context namely over hyperimaginaries, and it is shown that in a simple theory, Ltp ≡ stp in real context implies that for hyperimaginary context, and a question remains whether this holds in any theory. Expand
The Lascar groups and the first homology groups in model theory
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 $G$Expand
The structure of compact groups
The theme of this book is the Structure Theory of compact groups. It contains a completely selfcontained introduction to linear Lie groups and a substantial body of material on compact Lie groups.Expand
Galois Groups of First order Theories
TLDR
It is proved that EKP is the composition of EL and the closure of EL, and the associated equivalence relations EL and EKp, attached to a first order theory T. Expand
THE RELATIVIZED LASCAR GROUPS, TYPE-AMALGAMATIONS, AND ALGEBRAICITY
We apply compact group theory to obtain some model-theoretic results about the relativized Lascar Galois group of a strong type.
A Note on Lascar Strong Types in Simple Theories
TLDR
It is proved that for such T, the notion of Lascar strong type coincides with the concept of strong type, over an arbitrary set, in a countable, small simple theory. Expand
About The Lascar Group
Acknowledgements I am deeply grateful to Enrique Casanovas. It has been a pleasure to be guided by him throughout this years in such a constant and rigorous way; always dedicating lots of his time toExpand
Tits Buildings And The Model Theory Of Groups
...
1
2
...