Corpus ID: 235458629

Automorphism groups over a hyperimaginary

  title={Automorphism groups over a hyperimaginary},
  author={Byunghan Kim and Hyo-Tae Lee},
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


Hyperimaginaries and automorphism groups
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
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
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A Note on Lascar Strong Types in Simple Theories
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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
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