Geodesic
An arithmetical examples of a~non-Borel Luzin analytic set
Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 525-534.

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N. N. Luzin has constructed a sieve defining a screened non-Borel analytic set and has indicated the arithmetical properties of points of this set. In this article it is shown that a screened analytic set contains continuum number of points which do not have these arithmetical properties. Necessary and sufficient arithmetical conditions on points are found, under which they lie in a Luzin set screened by a sieve. 
@article{MZM_1977_22_4_a7,
     author = {M. A. Lunina},
     title = {An arithmetical examples of {a~non-Borel} {Luzin} analytic set},
     journal = {Matemati\v{c}eskie zametki},
     pages = {525--534},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a7/}
}
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M. A. Lunina. An arithmetical examples of a~non-Borel Luzin analytic set. Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 525-534. http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a7/