Add to ORKGIn this paper, we show that Frucht's theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic automorphism group of a $\mathbf{\Delta^0_2}$-graph on a Polish space
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
The subject matter of this Thesis is an instance of the Chain Condition Method of coarse classificat...
A nice example of how group theory deals with symmetry is Frucht's theorem that says that each finit...
The paper is devoted to the study of topologies on the group $\text{\rm Aut}(X,{\Cal B})$ of all Bor...
§1. Introduction. This paper considers several complexity questions regard-ing Borel automorphisms o...
When does Borel's theorem on free subgroups of semisimple groups generalize to other groups? We init...
AbstractThis paper consists essentially of the text of a series of four lectures given by the author...
This paper consists essentially of the text of a series of four lectures given by the author in the ...
This paper consists essentially of the text of a series of four lectures given by the author in the ...
Abstract. Suppose that G and H are Polish groups which act in a Borel fash-ion on Polish spaces X an...
To every graph (or digraph) A, there is an associated automorphism group Aut(A). Frucht’s theorem as...
AbstractLet Aut(X, B) be the group of all Borel automorphisms of a standard Borel space (X, B). We s...
This paper is a contribution to the study of Borel equivalence relations on standard Borel spaces (...
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
The subject matter of this Thesis is an instance of the Chain Condition Method of coarse classificat...
A nice example of how group theory deals with symmetry is Frucht's theorem that says that each finit...
The paper is devoted to the study of topologies on the group $\text{\rm Aut}(X,{\Cal B})$ of all Bor...
§1. Introduction. This paper considers several complexity questions regard-ing Borel automorphisms o...
When does Borel's theorem on free subgroups of semisimple groups generalize to other groups? We init...
AbstractThis paper consists essentially of the text of a series of four lectures given by the author...
This paper consists essentially of the text of a series of four lectures given by the author in the ...
This paper consists essentially of the text of a series of four lectures given by the author in the ...
Abstract. Suppose that G and H are Polish groups which act in a Borel fash-ion on Polish spaces X an...
To every graph (or digraph) A, there is an associated automorphism group Aut(A). Frucht’s theorem as...
AbstractLet Aut(X, B) be the group of all Borel automorphisms of a standard Borel space (X, B). We s...
This paper is a contribution to the study of Borel equivalence relations on standard Borel spaces (...
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a con...
The subject matter of this Thesis is an instance of the Chain Condition Method of coarse classificat...