Geodesic
Perfect subsets of invariant CA-sets
Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 334-338.

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The familiar theorem that any $\Sigma^1_2(a)$-set $X$ of real numbers (where $a$ is a fixed real parameter) not containing a perfect kernel necessarily satisfies the condition $X\subseteq\mathbf L[a]$ is extended to a wider class of sets, with countable ordinals allowed as additional parameters in $\Sigma^1_2(a)$-definitions. 
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V. G. Kanovei; V. A. Lyubetskii. Perfect subsets of invariant CA-sets. Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 334-338. http://geodesic.mathdoc.fr/item/MZM_2005_77_3_a1/

[1] Kanovei V. G., Lyubetskii V. A., “O nekotorykh klassicheskikh problemakh deskriptivnoi teorii mnozhestv”, UMN, 58:5 (2003), 3–88 | MR | Zbl

[2] Souslin M., “Sur une définition des ensembles mesurables B sans nombres transfinis”, C. R. Acad. Sci. Paris, 164 (1917), 88–90

[3] Lusin N., Sierpiński W., “Sur quelques propriétés des ensembles (A)”, Bull. Int. Acad. Sci. Cracowie, 4 (1918), 35–48; Лузин Н. Н., Собр. соч., Т. 2, Изд. АН СССР, М., 1958, 273–284

[4] Novikov P. S., “O neprotivorechivosti nekotorykh polozhenii deskriptivnoi teorii mnozhestv”, Tr. MIAN, 38, Nauka, M., 1951, 279–316

[5] Solovay R. M., “A model of set theory in which every set of reals is Lebesgue measurable”, Ann. Math., 92:1 (1970), 1–56 | DOI | Zbl

[6] Kanovei V. G., “Razvitie deskriptivnoi teorii mnozhestv pod vliyaniem trudov N. N. Luzina”, UMN, 40:3 (243) (1985), 117–153

[7] Uspenskii V. A., “Vklad N. N. Luzina v deskriptivnuyu teoriyu mnozhestv i funktsii: ponyatiya, problemy, predskazaniya”, UMN, 40:3 (243) (1985), 85–116

[8] Lyubetskii V. A., “Iz suschestvovaniya neizmerimogo mnozhestva tipa $A_2$ vytekaet suschestvovanie neschetnogo mnozhestva, ne soderzhaschego sovershennogo podmnozhestva, tipa CA”, Dokl. AN SSSR, 195:3 (1970), 548–550

[9] Lyubetskii V. A., “Nezavisimost nekotorykh predlozhenii deskriptivnoi teorii mnozhestv ot teorii mnozhestv Tsermelo–Frenkelya”, Vestn. MGU. Ser. 1. Matem., mekh., 1971, no. 2, 78–82

[10] Solovay R. M., “On the cardinality of $\Sigma^1_2$ sets”, Foundations of Mathematics, Symposium papers commemorating the 60th birthday of Kurt Gödel, Springer-Verlag, Berlin, 1969, 58–73

[11] Lyubetskii V. A., “Iz suschestvovaniya neizmerimogo mnozhestva tipa $A_2$ sleduet suschestvovanie neschetnogo mnozhestva tipa CA, ne soderzhaschego sovershennogo podmnozhestva”, Tezisy dokladov po algebre, matematicheskoi logike i vychislitelnoi matematike konferentsii ped. vuzov tsentr. zony RSFSR, Ivanovo, 1970, 22–24

[12] Kanovei V. G., Lyubetskii V. A., “O mnozhestve konstruktivnykh veschestvennykh chisel”, Tr. MIAN, 247, Nauka, M., 2004, 95–128