# The conjugacy problem for the automorphism group of the random graph

@article{Coskey2009TheCP, title={The conjugacy problem for the automorphism group of the random graph}, author={Samuel Coskey and Paul Ellis and Scott Schneider}, journal={Archive for Mathematical Logic}, year={2009}, volume={50}, pages={215-221} }

We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.

## 9 Citations

### Conjugacy for homogeneous ordered graphs

- MathematicsArch. Math. Log.
- 2019

It is shown that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is Borel complete and each such G satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of G are Borel reducible to the conjugal relation on automorphism of G.

### Conjugacy for homogeneous ordered graphs

- MathematicsArchive for Mathematical Logic
- 2018

We show that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is Borel complete. In fact we establish that each such G satisfies a strong extension property…

### On the classification of automorphisms of trees

- MathematicsContributions Discret. Math.
- 2019

The complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy is identified and the complexity ofThe conjugate problem in the case of automorphism of several non-regularly branching trees is calculated.

### The conjugacy problem for automorphism groups of homogeneous digraphs

- MathematicsContributions Discret. Math.
- 2017

The Borel complexity of the conjugacy problem for automorphism groups of countable homogeneous digraphs is decided, and a dichotomy theorem is established that this complexity is either the minimum or the maximum among relations which are classifiable by countable structures.

### The Complexity of Classification Problems for Models of Arithmetic

- MathematicsThe Bulletin of Symbolic Logic
- 2010

It is shown that the classification problem for countable models of arithmetic is Borel complete and for automorphisms of a fixed recursively saturated model are Borelcomplete.

### Elements of finite order in automorphism groups of homogeneous structures

- MathematicsContributions Discret. Math.
- 2013

These constructions enable us to compute the Borel complexity of the relation of conjugacy between automorphisms of the Henson graphs, and to obtain some new results about the structure of the isometry group of the Urysohn space and the URYsohn sphere.

### RESEARCH PROPOSAL: BOREL EQUIVALENCE RELATIONS

- Mathematics
- 2010

The study of definable equivalence relations on complete separable metric spaces (i.e., Polish spaces) has emerged as a new direction of research in descriptive set theory over the past twenty years.…

### Polish groups and Baire category methods

- Mathematics
- 2016

This memoir presents my work since the end of my doctoral work. The unifying theme is the use of Baire category methods in various domains where Polish groups appear naturally.

### The conjugacy problem for automorphism groups of countable homogeneous structures

- MathematicsMath. Log. Q.
- 2016

In each case, the precise complexity of the conjugacy relation in the sense of Borel reducibility of automorphism groups of a number of countable homogeneous structures is found.

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