Geodesic
On a~universal Borel adic space
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 24-38

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We prove that the so-called uniadic graph and its adic automorphism are Borel universal, i.e., every aperiodic Borel automorphism is isomorphic to the restriction of this automorphism to a subset invariant under the adic transformation, the isomorphism being defined on a universal (with respect to the measure) set. We develop the concept of basic filtrations and combinatorial definiteness of automorphisms suggested in our previous paper. 
@article{ZNSL_2018_468_a2,
     author = {A. M. Vershik and P. B. Zatitskii},
     title = {On a~universal {Borel} adic space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {24--38},
     publisher = {mathdoc},
     volume = {468},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a2/}
}
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A. M. Vershik; P. B. Zatitskii. On a~universal Borel adic space. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 24-38. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a2/