Geodesic
Isolation: motivations and applications
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 204-217

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In this paper, we briefly review the origins of the isolation phenomenon and its applications. We discuss a stronger notion of double bubbles. We also show recent achievements in the study of lattice embeddings with the help of the isolation property.
Keywords: Turing degrees, Ershov hierarchy, isolated degrees, lattice embeddings. 
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G. Wu; M. M. Yamaleev. Isolation: motivations and applications. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 204-217. http://geodesic.mathdoc.fr/item/UZKU_2012_154_2_a19/