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YErshov YU.L.




     *bibliography + data base
     *his life and work
     *Selected works (Rus)



 Schools of thought in NSC

Literature on his life and workInternet Index of works
 
1963 | 1971 | 1972 | 1975 | 1983 | 1985 | 1988 | 1990 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |

  1. Soloukhin R. Pyervyye diplomy / R.Soloukhin // Za nauku v Sibiri. - 1963. - N 50 (23 dyekabrya).

  2. Dyenisov S.D. Modyeli nyeprotivoryechivoi formuly i iyerarkhiya YErshova // Algyebra i logika. - 1971.- T.11, N 6. – C.648-655.

  3. Dyenisov S.D. Modyeli nyeprotivoryechivoi formuly i iyerarkhiya YErshova / S.D.Dyenisov // Algyebra i logika. - 1972. - T.11, N 6. - S.648-655.

  4. Denisov S.D. Models of noncontradictory formulas and the Ershov hierarchy / S.D.Denisov // Algebra Logika. - 1972. - Vol.11, N 6. - P.359-362.

  5. Palyutin YE.A. Dopolnyeniye k stat'ye YU.L.YErshova «Vyerkhnyaya poluryeshyetka numyeratsii konyechnogo mnozhyestva» / YE.A.Palyutin // Algyebra i logika. - 1975. - T.14, N 3. - S.284-287.

  6. CHaikin S. Uchyenik Mal'tsyeva / S.CHaikin // Za nauku v Sibiri. - 1975. - 24 apryelya.

  7. Palyutin E.A. Supplement to Yu.L.Ershov's article «The upper semilattice of numerations of a finite set» / E.A.Palyutin // Algebra Logika. - 1975. - Vol.14, N 3. - P.176-178.

  8. Mohrherr J. A conjecture of Ershov for a relative hierarchy fails near o' / J.Mohrherr // Algebra Logika. - 1983. - Vol.22, N 2. - P.232–235.

  9. Selivanov V.L. Ershov hierarchy / V.L.Selivanov // Siberian Mathematical Journal. - 1985. - Vol.26, N 1. - P.105-117.

  10. Syelivanov V.L. Iyerarkhiya YErshova i T-skachok / V.L.Syelivanov // Algyebra i logika. - 1988. - T.27, N 4. - S.464-478.

  11. Selivanov V.L. Ershov hierarchy and the t-jump / V.L.Selivanov // Algebra Logika. - 1988. - Vol.27, N 4. - P.292-301.

  12. YUrii Lyeonidovich YErshov: (k pyatidyesyatilyetiyu so dnya rozhdyeniya) // Algyebra i logika. – 1990. - T.29, N2. - S.135-138.

  13. YUrii Lyeonidovich YErshov: (k pyatidyesyatilyetiyu so dnya rozhdyeniya) // Sibirskii matyematichyeskii zhurnal. - 1990. - T.31, N3. - S.455-457.

  14. YErshov YUrii Lyeonidovich // Matyematichyeskii ehntsiklopyedichyeskii slovar'. - M.: Bol'shaya Rossiiskaya ehntsiklopyediya, 1995. - C.693.

  15. Goncharov S.S. Syemyeistva s odnoehlyemyentnoi poluryeshyetkoi Rodzhyersa / S.S.Goncharov, S.A.Badayev; NII mat.-inf. osnov obuch. Novosib. gos. un-ta // Pryeprint. - 1996. - N 15. - S. 1-26.
    Rabota posvyascyena ryeshyeniyu zadachi YU.L.YErshova - opisaniya syemyeistva s odnoehlyemyentnoi poluryeshyetkoi vychislimykh numyeratsii (poluryeshyetkoi Rodzhyersa). Poluchyeno algoritmichyeskoye opisaniye syemyeistva obscyeryekursivnykh funktsii s odnoehlyemyentnymi poluryeshyetkami Rodzhyersa. Dokazano suscyestvovaniye nyetrivial'nogo syemyeistva ryekursivno pyeryechislimykh mnozhyestv, sodyerzhascyego naimyen'shyeye po vklyuchyeniyu mnozhyestvo, poluryeshyetka Rodzhyersa kotorogo odnoehlyemyentna.

  16. Goncharov S.S. Schyetnyye bulyevy algyebry i razryeshimost' / S.S.Goncharov. - Novosibirsk: Nauchnaya kniga, 1996. - 361 s.
    Suscyestvyenno pyeryerabotannaya i dopolnyennaya novymi ryezul'tatami vyersiya knigi avtora «Schyetnyye bulyevy algyebry» (sm. RZHMat, 1989, 4A229K). Algyebraichyeskiye osnovy tyeorii bulyevykh algyebr izlagayutsya na osnovye krityeriya Voota i dokazatyel'stva YErshova klassifikatsii Kyetonyena. Izuchayutsya ehlyemyentarnyye tyeorii i algoritmichyeskiye svoistva bulyevykh algyebr. Dyemonstriruyetsya primyenyeniye razlichnykh myetodov, v chastnosti, myetody schyetnykh nasyscyennykh modyelyei, razryeshimykh odnorodnykh modyelyei i vyetvyascikhsya modyelyei, a takzhye pryedstavlyeny podkhody k izuchyeniyu proizvodnykh struktur: ryeshyetok podalgyebr, grupp avtomorfizmov i vychislimykh klassov.

  17. Palmgren E. A logical presentation of the continuous functionals / E.Palmgren // The Journal of Symbolic Logic. - 1997. - Vol.62, N 3. - P.1021-1034.
    Pryedlozhyena, v dopolnyeniye k izvyestnym, yescye odna kharaktyerizatsiya nyepryeryvnykh funktsionalov Klini-Kryeisyela, nazvannaya tyeoryetiko-modyel'noi, a faktichyeski tyesno svyazannaya s podkhodom YErshova, osnovannym na oblastyakh Skotta-YErshova.

  18. Syelivanov V.L. Ob iyerarkhii YErshova v behrovskom prostranstvye / V.L.Syelivanov // 3-i Sibirskii kongryess po prikladnoi i industrial'noi matyematikye (INPRIM-98). - Novosibirsk: Izd-vo IM SO RAN, 1998. - Syektsiya: Algyebra, CH. 5. - S.28.

  19. Omarov A.I. Ob odnom krityerii ω-1 nasyscyennosti algyebry YErshova / A.I.Omarov // Matyerialy Myezhdunarodnoi konfyeryentsii po matyematichyeskoi logikye, posvyascyennoi 90-lyetiyu so dnya rozhdyeniya A.I.Mal'tsyeva i 275-lyetiyu Rossiiskoi akadyemii nauk, Novosibirsk, 1999. - Novosibirsk, 1999. - S.45-46.

  20. Trofimov A.V. EHlyemyentarnyye svoistva obogascyennykh algyebr YErshova / A.V.Trofimov // Matyerialy Myezhdunarodnoi konfyeryentsii po matyematichyeskoi logikye, posvyascyennoi 90-lyetiyu so dnya rozhdyeniya A.I.Mal'tsyeva i 275-lyetiyu Rossiiskoi akadyemii nauk, Novosibirsk, 1999. - Novosibirsk, 1999. - S.59-61.

  21. YUrii Lyeonidovich YErshov: (k 60-lyetiyu so dnya rozhdyeniya) / M.M.Lavryent'yev, V.L.Byeryesnyev, A.A.Borovkov, S.K.Godunov, S.S.Goncharov, V.D.Mazurov, S.S.Kutatyeladzye, YU.G.Ryeshyetnyak, V.G.Romanov // Sibirskii matyematichyeskii zhurnal. - 2000. - T.41, N 2. - S.243-246.

  22. YUrii Lyeonidovich YErshov: k shyestidyesyatilyetiyu so dnya rozhdyeniya / S.S.Goncharov, I.A.Lavrov, V.D.Mazurov, A.A.Mal'tsyev, A.S.Morozov, A.A.Nikitin, YE.A.Palyutin, D.M.Smirnov // Vladikavkazskii matyematichyeskii zhurnal. - 2000. - T.2, N 2. - S.3-9.

  23. Lidyer sibirskoi shkoly algyebry i logiki / S.S.Goncharov, I.A.Lavrov, V.D.Mazurov, A.A.Mal'tsyev, A.S.Morozov, A.A.Nikitin, YE.A.Palyutin, D.M.Smirnov // Nauka v Sibiri. – 2000. - N 17 (28 apryelya).

  24. O nagrazhdyenii ordyenom «Za zaslugi pyeryed otyechyestvom» IV styepyeni YErshova YU.L.: ukaz Pryezidyenta RF ot 28.04.2000 N 774 // Sobraniye zakonodatyel'stva Rossiiskoi Fyedyeratsii. - 2000. - Vyp. 18. - St. 1976.

  25. S YUbilyeyem: [akadyemiku YUriyu Lyeonidovichu YErshovu - 60 lyet!] // Nauka v Sibiri. - 2000. - N 17 (2253).

  26. Trofimov A.V. Tipy izomorfizma obogascyennykh supyeratomnykh algyebr YErshova / A.V.Trofimov // Matyematichyeskiye trudy. - 2000. - T.3, N 2. - S.182-201.

  27. SHmatkov M.N. Dokazatyel'stvo tyeoryemy polnoty ischislyeniya dinamichyeskoi logiki DL / M.N.SHmatkov // Vyestnik YUzhno-Ural'skogo gosudarstvyennogo univyersityeta. Syer.: matyematika, fizika, khimiya. - 2001. - N 7. - S.24-34.
    Rassmatrivayutsya voprosy, otnosyasciyesya k tyeorii vychislimosti. Provoditsya podrobnoye dyetal'noye dokazatyel'stvo tyeoryemy o polnotye ischislyeniya dinamichyeskoi logiki DL, privyedyennoi YU. L.YErshovym v rabotye: Opryedyelimost' i vychislimost' (Novosibirsk, 1996)

  28. Puzaryenko V.G. O razryeshimykh vychislimykh A-numyeratsiyakh / V.G.Puzaryenko // Algyebra i logika. - 2002. - T.41, N 5. - S.568-584.
    Rassmatrivayutsya numyeratsii na dopustimykh mnozhyestvakh, kotoryye YU.L.YErshov vvyel v knigye «Opryedyelimost' i vychislimost'». Dlya modyelyei dvukh spyetsial'nykh klassov ryeshayetsya problyema suscyestvovaniya odnoznachnykh vychislimykh numyeratsii syemyeistv vsyekh vychislimykh mnozhyestv i vychislimykh funktsii. V pyervom sluchaye pri dokazatyel'stvye konyechnymi ob'yektami sluzhat sintaksichyeskiye konstruktsii, a vo vtorom – konyechnyye podmnozhyestva naslyedstvyenno konyechnoi nadstroiki.

  29. Samokhvalov K.F. «Novyi podkhod» YErshova i «transtsyendyental'nyi myetod» Kanta / K.F.Samokhvalov // Vychislityel'nyye sistyemy. - 2002. - N 172. - S.22-55.

  30. Trudy Myezhdunarodnoi konfyeryentsii «Logika i Prilozhyeniya», posvyascyennoi 60-lyetiyu so dnya rozhdyeniya YU.L.YErshova i Myezhdunarodnoi konfyeryentsii po matyematichyeskoi logikye, posvyascyennoi 90-lyetiyu so dnya rozhdyeniya A.I.Mal'tsyeva i 275-lyetiyu RAN - Novosibirsk, 2002. - 244 c.

  31. Arslanov M. Models of relative computability and the Ershov hierarchy / M.Arslanov // Bulletin of Symbolic Logic. - 2002. - Vol.8, N 1. - P.124.
    Obsuzhdayetsya opryedyelimost' ryekursivnoi pyeryechislimosti i otnosityel'noi ryekursivnoi pyeryechislimosti v strukturye n- r.p. styepyenyei dlya n1

  32. Cooper S.B. Turing definability in the Ershov hierarchy / S.B.Cooper, Li Angsheng // Journal of the London Mathematical Society. - 2002. - Vol.66, N 3. - P.513-528.
    V tyeorii t'yuringovykh styepyenyei znachityel'noye myesto zanimayut voprosy opryedyelimosti po T'yuringu odnikh klassov styepyenyei vnutri drugikh. Primyerom takogo voprosa yavlyayetsya vopros o tom, opryedyelim li klass E pyeryechislimykh styepyenyei vnutri klassa DCE-styepyenyei (izvyestnykh takzhye kak 2-pyeryechislimyye styepyeni). CHasto v kachyestvye priblizhyeniya k ryeshyeniyu takikh zadach pokazyvayetsya opryedyelimost' nye samogo rassmatrivayemogo klassa, a sodyerzhascyego yego ili sodyerzhascyegosya v nyem.

  33. Khisamiev A.N. On quasiresolvable models and B-models Khisamiev // Bulletin of Symbolic Logic. - 2002. - Vol.8, N 1. - P.170-171.
    Obsuzhdayutsya sootnoshyeniya myezhdu klassami ryezol'vyentnykh mnozhyestv, kvaziryezol'vyentnykh dopustimykh mnozhyestv, vnutryennye pyeryechislimykh modyelyei i B-modyelyei (pyervyye dva klassa vvyel YU.L.YErshov, a poslyedniye dva - avtor doklada). V chastnosti, anonsiruyetsya krityerii vnutryennyei pyeryechislimosti v tyerminakh kvaziryezol'vyentnosti

  34. Puzarenko V.G. Decidable Computable A-Numberings / V.G.Puzarenko // Algebra and Logic. - 2002. - Vol.41, N 5. - P.314-322.
    The article deals in the numbering theory for admissible sets, brought in sight in Yu.L.Ershov's «Definability and Computability» atv «Numbering Theory». For models of two special classes, we resolve the problem of there being 1-1 computable numberings of the families of all computable sets and of all computable functions. In proofs, for the former case the role of finite objects is played by syntactic constructions, and for the latter - by finite subsets on hereditarily finite superstructures.

  35. Talasbaeva Zh. On positive numberings in Ershov's hierarchy / Zh.Talasbaeva // Bulletin of Symbolic Logic. - 2002. - Vol.8, N 1. - P.178.

  36. Murzina V.F. Modal'naya logika na osnovye linyeino uporyadochyennykh ƒ-prostranstv / V.F.Murzina // Algyebra i logika. - 2003. - T.42, N 3. - S.320-337.
    Rassmatrivayetsya modal'naya logika, svyazannaya s ƒ-prostranstvami, vvyedyennymi YU.L.YErshovym. Stroitsya modal'noye ischislyeniye, polnoye otnosityel'no klassa vsyekh strogo linyeino uporyadochyennykh ƒ0-shkal i otnosityel'no klassa vsyekh strogo linyeino uporyadochyennykh ƒ-shkal.

  37. Samokhvalov K.F. «Novyi podkhod» YErshova i «transtsyendyental'nyi myetod» Kanta / K.F.Samokhvalov // Matyematika i opyt. - M.: MGU, 2003. - S.174-204.

  38. Talasbayeva ZH.T. O pozitivnykh numyeratsiyakh syemyeistv mnozhyestv iyerarkhii YErshova / ZH.T.Talasbayeva // Algyebra i logika. - 2003. - T.42, N 6. - S.737-746.
    Dokazyvayetsya suscyestvovaniye byeskonyechnogo chisla pozitivnykh nyerazryeshimykh Σn-1-vychislimykh numyeratsii lyubogo byeskonyechnogo syemyeistva S vklyuchyennogo ili ravnogo Σn-1, kotoroye dopuskayet khotya by odnu Σn-1-vychislimuyu numyeratsiyu i sodyerzhit libo pustoye mnozhyestvo pri chyetnom n, libo N pri nyechyetnom n

  39. O prisuzhdyenii Gosudarstvyennykh pryemii Rossiiskoi Fyedyeratsii 2002 goda v oblasti nauki i tyekhniki: ukaz Pryezidyenta Rossiiskoi Fyedyeratsii ot 13.12.2003 g. N 1481 // Sobraniye zakonodatyel'stva Rossiiskoi Fyedyeratsii. - 2003. - Vyp. 5. - St.4878.
    Prisudit' Gosudarstvyennyye pryemii Rossiiskoi Fyedyeratsii 2002 goda v oblasti nauki i tyekhniki i prisvoit' zvaniye lauryeata Gosudarstvyennoi pryemii Rossiiskoi Fyedyeratsii v oblasti nauki i tyekhniki: … 6. YErshovu YUriyu Lyeonidovichu, akadyemiku, diryektoru gosudarstvyennogo nauchno-isslyedovatyel'skogo uchryezhdyeniya «Institut diskryetnoi matyematiki i informatiki», - za monografiyu «Kratno normirovannyye polya»

  40. Murzina V.F. A Modal Logic Based on Linearly Ordered ƒ-Spaces / V.F.Murzina // Algebra Logika. - 2003. - Vol.42, N 3. - P.181-191.
    A modal logic associated with the ƒ-spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered ƒ0-frames, and the class of all strictly linearly ordered ƒ-frames.

  41. Talasbaeva Z.T. Positive Numberings of Families of Sets in the Ershov Hierarchy / Z.T.Talasbaeva // Algebra Logika. - 2003. - Vol.42, N 6. - P.413-418.
    It is proved that there exist infinitely many positive undecidable Σn-1-computable numberings of every infinite family S included or equally Σn-1, that admits at least one Σn-1-computable numbering and contains either the empty set, for even n, or N for odd n.

  42. Frolov A.N. Konstruktiviziruyemost' struktur i ikh styepyeni nyerazryeshimosti: avtoryefyerat dis. soisk. uch. styep. kand. fiz.-mat. nauk / A.N.Frolov. - Novosibirsk, 2004. - 8 s.
    V dissyertatsii izuchayutsya konstruktiviziruyemyye linyeinyye poryadki, algyebry YErshova i drugiye struktury

  43. KHisamiyev A.N. O vyerkhnyei poluryeshyetkye YErshova LE / A.N.KHisamiyev // Sibirskii matyematichyeskii zhurnal. - 2004. - T.45, N 1. - S.211-228.
    Naidyeny svyazi myezhdu Σ-svodimost'yu i T-svodimost'yu. Dokazany utvyerzhdyeniya: 1) yesli kvazizhyestkaya modyel' sil'no Σ-opryedyelima v naslyedstvyenno konyechnom dopustimom mnozhyestvye nad lokal'no konstruktiviziruyemoi B-sistyemoi, to ona konstruktiviziruyema; 2) kazhdaya abyelyeva p-gruppa i algyebra YErshova lokal'no konstruktiviziruyemy; 3) yesli antisimmyetrichnaya svyazannaya modyel' Σ-opryedyelima v naslyedstvyenno konyechnom dopustimom mnozhyestvye nad schyetnoi algyebroi YErshova, to ona konstruktiviziruyema.

  44. Khisamiev A.N. On the Ershov Upper Semilattice LE / A.N.Khisamiev // Siberian Mathematical Journal. - 2004. - Vol.45, N 1. - P.173-187.
    We find some links between Σ-reducibility and T-reducibility. We prove that (1) if a quasirigid model is strongly Σ-definable in a hereditarily finite admissible set over a locally constructivizable B-system, then it is constructivizable; (2) every abelian p-group and every Ershov algebra is locally constructivizable; (3) if an antisymmetric connected model is Σ-definable in a hereditarily finite admissible set over a countable Ershov algebra then it is constructivizable.

  45. Murzina V. The completeness theorem for temporal logic based on strictly ordered ƒ-spaces / V.Murzina // Bulletin of Symbolic Logic. - 2004. - Vol.10, N 2. - P.267.
    Obsuzhdayutsya linyeino uporyadochyennyye ƒ-prostranstva, ƒ-0-prostranstva YErshova i sootvyetstvuyusciye im vryemyennyye shkaly (v stilye Kripkye) s otnoshyeniyem strogogo poryadka R

  46. YErshov YUrii Lyeonidovich // Rossiiskaya akadyemiya nauk. Sibirskoye otdyelyeniye: pyersonal'nyi sostav. - Novosibirsk: Nauka, 2007. - S.86-87.

  47. Murzina V.F. Otsutstviye intyerpolyatsionnogo svoistva dlya vryemyennykh ischislyenii, svyazannykh s prostranstvami YErshova / V.F.Murzina // Algyebra i logika. - 2007. - T.46, N 6. - S.745-762.
    Isslyeduyetsya vopros, obladayut li intyerpolyatsionnym svoistvom Kryeiga ischislyeniya, svyazannyye s topologichyeskimi prostranstvami YErshova.

  48. Murzina V.M. Freedom from the interpolation property for tense calculi associated with Ershov spaces / V.M.Murzina // Algebra Logika. - 2007. - Vol.46, N 6. - P.409-418.
    We study into the question whether calculi associated with Ershov topological spaces possess Craig's interpolation property.

  49. Batyrshin I.I. Otnosityel'naya pyeryechislimost' v iyerarkhii YErshova / I.I.Batyrshin // Matyematichyeskiye zamyetki. - 2008. - T.84, N 4. - S.506-515.
    V rabotye privodyatsya ryezul'taty, kasayusciyesya obobscyenii na drugiye urovni iyerarkhii YErshova nyekotoroi tyeoryemy o svyazi n-vychislimoi pyeryechislimosti i otnosityel'noi pyeryechislimosti.

  50. Batyrshin I.I. Relative enumerability in Ershov's hierarchy / I.I.Batyrshin // Mathematical notes. - 2008. - Vol.84, N 3-4. - P.473-482.
    Generalizations to various levels of Ershov's hierarchy of the relationship between n-computable enumerability and relative enumerability are considered.

  51. Batyrshin I.I. Svoistva kvazi-svodimosti i iyerarkhii YErshova: avtoryefyerat dis. na soisk. uch. styep. kand. fiz.-mat. nauk / I.I.Batyrshin. - Kazan', 2009. - 12 s.

  52. Akadyemiku YU.L.YErshovu - 70 lyet // Vyestnik Rossiiskoi akadyemii nauk. - 2010. - T.80, N 8. - S.757-758.

  53. Asyeyev A.L. K 70-lyetiyu akadyemika YU.L.YErshova / A.L.Asyeyev, N.Z.Lyakhov, B.G.Mikhailyenko // Nauka v Sibiri. - 2010. - N 17 (29 apryelya). - C.2.

  54. Brat'ya-akadyemiki: vsyu zhizn' plyechom k plyechu: o Valyerii Lyeonidovichye Makarovye i YUrii Lyeonidovichye YErshovye // ZHurnal byudzhyet. - 2010. - N 4. - S.76-79.

  55. Goncharov S.S. Slovo ob uchityelye / S.S.Goncharov // Nauka v Sibiri. - 2010. - N 17 (29 apryelya). - S.10.
    O vydayuscyemsya matyematikye YU.L.YErshovye i osnovnykh napravlyeniyakh yego dyeyatyel'nosti

  56. Gotovy otvyetit' trudom // Nauka v Sibiri. - 2010. - N 30-31 (2765-2766). - S.2.

  57. Diyev V.S. CHyelovyek dvukh kul'tur / V.S.Diyev // Nauka v Sibiri. - 2010. - N 17 (2752). - S.10.
    O dyeyatyel'nosti YUriya Lyeonidovicha YErshova rasskazyvayet V.S. Diyev, d.f.n. profyessor, dyekan filosofskogo fakul'tyeta NGU.

  58. YErshov YUrii Lyeonidovich (k syemidyesyatilyetiyu so dnya rozhdyeniya) / S.S.Goncharov, A.G.Kusrayev, S.S.Kutatyeladzye, I.A.Lavrov, V.D.Mazurov, A.S.Morozov, M.V.Syemenova // Vladikavkazskii matyematichyeskii zhurnal. - 2010. - T.12, N 2. - S.75-78.

  59. YUrii Lyeonidovich YErshov (ko dnyu 70-lyetiya) // Algyebra i logika. - 2010. - T.49, N 6. - S.i-v.

  60. YUrii Lyeonidovich YErshov. K 70-lyetiyu so dnya rozhdyeniya // Sibirskii matyematichyeskii zhurnal. - 2010. - T.51, N 3. - S.477-480.

  61. YErshov YU.L. «YA nikogda nye zhalyel o svoyem vyborye» / YU.L.YErshov; podgotovila M.Goryntsyeva // Nauka v Sibiri. - 2010. - N 17, (2752). - S.9.
    Akadyemiku YUriyu Lyeonidovichu YErshovu 1 maya ispolnyayetsya 70 lyet. Nakanunye yubilyeya YU.L.YErshov priglasil pryedstavityelyei pryessy, chtoby otvyetit' na voprosy i rasskazat' o syebye, svoyei zhizni i rabotye.

  62. Kutatyeladzye S.S. Svyetila i sputniki. (k 70-lyetiyu so dnya rozhdyeniya YU.L.YErshova) / S.S.Kutatyeladzye // Sibirskii zhurnal industrial'noi matyematiki. - 2010. - T.13, N 2. - S.3-4.

  63. Nadtochii A. Iyerarkhiya YErshova: shtrikhi k portryetu yubilyara / A.Nadtochii // Vyechyernii Novosibirsk. - 2010. - 29 apryelya (N 73). - S.10-11.

  64. Nadtochii N. Kak stat' vydayuscimsya uchyenym: «posobiye» dlya nachinayuscyego k 70-lyetiyu akadyemika YUriya YErshova / N.Nadtochii // Sovyetskaya Sibir'. - 2010. - N 81.

  65. Ospichyev S.S. Nyekotoryye svoistva numyeratsii razlichnykh klassov iyerarkhii YErshova / S.S.Ospichyev // Vyestnik NGU. Syeriya: matyematika, myekhanika, informatika. - 2010. - T.10, N 4. - S.125-132.

  66. O prisuzhdyenii pryemii Pravityel'stva Rossiiskoi Fyedyeratsii 2010 goda v oblasti obrazovaniya: rasporyazhyeniye Pravityel'stva Rossiiskoi Fyedyeratsii ot 25.10.2010 g. N 1868-r // Sobraniye zakonodatyel'stva Rossiiskoi Fyedyeratsii. - 2010. - Vyp. 44. - St.5736.
    YU.L.YErshova prisuzhdyena pryemiya Pravityel'stva Rossiiskoi Fyedyeratsii za tsikl trudov «Kontsyeptsiya formirovaniya logiko-matyematichyeskogo obrazovaniya v vysshyei shkolye»

  67. O nagrazhdyenii gosudarstvyennymi nagradami Rossiiskoi Fyedyeratsii: ukaz Pryezidyenta Rossiiskoi Fyedyeratsii ot 16.06.2010 g. N 745 // Sobraniye zakonodatyel'stva Rossiiskoi Fyedyeratsii. - 2010. - Vyp.25. - St.3148.
    Za bol'shoi vklad v razvitiye nauki i mnogolyetnyuyu plodotvornuyu dyeyatyel'nost' nagradit' Ordyenom «Za zaslugi pyeryed Otyechyestvom» III Styepyeni YErshova YUriya Lyeonidovicha - akadyemika Rossiiskoi akadyemii nauk, diryektora Uchryezhdyeniya Rossiiskoi akadyemii nauk Instituta matyematiki imyeni S.L.Sobolyeva Sibirskogo otdyelyeniya RAN, gorod Novosibirsk

  68. Faizrakhmanov M.KH. Vychislimyye numyeratsii syemyeistv nizkikh mnozhyestv i t'yuringovy skachki v iyerarkhii YErshova / M.KH.Faizrakhmanov // Sibirskii matyematichyeskii zhurnal. - 2010. - T.51, N 6. - S.1435-1439.
    Poluchyen slyeduyuscii ryezul'tat, yesli dany Δ20-vychislimyye numyeratsii ν, μ syemyeistv mnozhyestv natural'nykh chisyel, to pryedikat P(x,y) ↔ ν(x) ≠ μ(y) yavlyayetsya Σ20-pryedikatom. Kak slyedstviya iz ehtogo ryezul'tata mozhno poluchit' dostatochnoye usloviye Δ20-suscyestvovaniya Δ20-vychislimoi numyeratsii podsyemyeistva vsyekh mnozhyestv dannogo syemyeistva, t'yuringovy skachki kotorykh lyezhat v fiksirovannom urovnye iyerarkhii YErshova, i suscyestvovaniye Σω-1-vychislimoi numyeratsii syemyeistva vsyekh supyernizkikh mnozhyestv.

  69. Faizrakhmanov M.KH. Razlozhimost' nizkikh 2-vychislimo pyeryechislimykh styepyenyei i t'yuringovyye skachki v iyerarkhii YErshova / M.KH.Faizrakhmanov // Izvyestiya vysshikh uchyebnykh zavyedyenii. Matyematika. - 2010. - N 12. - S.58-66.
    V rabotye dokazana tyeoryema: dlya kazhdogo oboznachyeniya konstruktivnogo ordinala suscyestvuyet nizkaya 2-vychislimo pyeryechislimaya styepyen', nye yavlyayuscayasya razlozhimoi na dvye myen'shiye 2-vychislimo pyeryechislimyye styepyeni, skachki kotorykh prinadlyezhat Δ-urovnyu iyerarkhii YErshova, sootvyetstvuyuscyemu ehtomu oboznachyeniyu.

  70. KHisamiyev A.N. ∑-ogranichyennyye algyebraichyeskiye sistyemy i univyersal'nyye funktsii / A.N.KHisamiyev // Sibirskii matyematichyeskii zhurnal. - 2010. - T.51, N 3. - S.676-693.
    Dokazano, chto lyubyye algyebry YErshova, bulyevy algyebry i abyelyevy p-gruppy yavlyayutsya Σ-ogranichyennymi sistyemami i v naslyedstvyenno konyechnykh dopustimykh mnozhyestvakh nad nimi suscyestvuyut univyersal'nyye Σ-funktsii.

  71. KHisamiyev A.N. Σ-ogranichyennyye algyebraichyeskiye sistyemy i univyersal'nyye funktsii / A.N.KHisamiyev // Doklady Rossiiskoi akadyemii nauk. - 2010. - T.431, N 6. - S.747-750.
    Obscyeprinyataya (absolyutnaya) tyeoriya vychislimosti izuchayet vychislimyye funktsii i otnoshyeniya na natural'nykh chislakh. V nastoyascyeye vryemya imyeyutsya razlichnyye obobscyeniya ponyatiya vychislimosti. V dannoi rabotye vvyedyeno ponyatiye Σ-ogranichyennoi algyebraichyeskoi sistyemy. Dokazano, chto algyebra YErshova, bulyeva algyebra, linyeinyi poryadok i abyelyeva p-gruppa yavlyayutsya Σ-ogranichyennymi sistyemami i v naslyedstvyenno konyechnykh dopustimykh mnozhyestvakh nad nimi suscyestvuyut univyersal'nyye Σ-funktsii

  72. SHkol'nik M. Nauki mnogo nye byvayet / M.SHkol'nik // Navigator. - 2010. - N 16 (30 apryelya ).
    V pryeddvyerii 70-lyetiya YUrii Lyeonidovich YErshov podyelilsya s pryessoi svoimi myslyami o proshlom, nastoyascyem i buduscyem rossiiskoi nauki.

  73. Faizrakhmanov M.Kh. Computable numberings of families of low sets and Turing jumps in the Ershov hierarchy / M.Kh.Faizrakhmanov // Siberian Mathematical Journal. - 2010. - Vol.51, N 6. - P.1135-1138.
    If n and m are some Δ20-computable numberings of families of sets of the naturals then P(x,y) ↔ ν(x) ≠ μ(y) is a Σ20-predicate. Deriving corollaries from this result, we obtain a sufficient condition for existence of a Δ20-computable numbering of the subfamily of all sets in a given family with the Turing jumps belonging to a fixed level of the Ershov hierarchy, and we deduce existence of a Σω-1-computable numbering of the family of all superlow sets

  74. Faizrakhmanov M.Kh. Decomposability of low 2-computably enumerable degrees and turing jumps in the Ershov hierarchy / M.Kh.Faizrakhmanov // Russian Mathematics. - 2010. - Vol.54, N 12. - P.51–58.
    In this paper we prove the following theorem: for every notation of a constructive ordinal there exists a low 2-computably enumerable degree that is not splittable into two lower 2-computably enumerable degrees whose jumps belong to the corresponding Δ-level of the Ershov hierarchy.

  75. Khisamiev A.N. Σ-bounded algebraic systems and universal functions. II / A.N.Khisamiev // Siberian Mathematical Journal. – 2010. - Vol.51, N 3. – P.537–551.
    Ershov algebras, Boolean algebras, and abelian p-groups are Σ-bounded systems, and there exist universal Σ-functions in hereditarily finite admissible sets over them.

  76. Arslanov M.M. Tyeoryetiko-modyel'nyye svoistva t'yuringovykh styepyenyei raznostnoi iyerarkhii YErshova / M.M.Arslanov // Sovryemyennyye problyemy matyematiki. - M.: MIAN, 2011. - Vyp.15: konfyeryentsiya «Mal'tsyevskiye chtyeniya». - S.5-14.

  77. Lyeont'yeva M.N. Bulyevy algyebry ehlyemyentarnoi kharaktyeristiki (1,0,1) s vychislimymi mnozhyestvom atomov i idyealom YErshova-Tarskogo / M.N.Lyeont'yeva // Algyebra i logika. - 2011. - T.50, N 2. - S.133-151.
    Dokazyvayetsya suscyestvovaniye vychislimoi bulyevoi algyebry ehlyemyentarnoi kharaktyeristiki (1,0,1) s vychislimymi mnozhyestvom atomov i idyealom YErshova-Tarskogo, u kotoroi nyet sil'no vychislimoi izomorfnoi kopii. Privoditsya takzhye nyekotoroye opisaniye Δ60-vychislimykh bulyevykh algyebr.

  78. Manat M. Pozitivnyye nyerazryeshimyye numyeratsii v iyerarkhii YErshova / M.Manat, A.Sorbi // Algyebra i logika. - 2011. - T.50, N 6. - S.759-780.
    Privoditsya dostatochnoye usloviye, pri kotorom byeskonyechnoye vychislimoye syemyeistvo ∑α-1-mnozhyestv imyeyet vychislimyye pozitivnyye, no nyerazryeshimyye numyeratsii, zdyes' a oboznachayet nyenulyevoi vychislimyi ordinal. EHto obobscayet tyeoryemu Talasbayevoi [Algyebra i logika, 42, N 6 (2003), 737-746], dokazannuyu dlya konyechnykh urovnyei iyerarkhii YErshova. Kak slyedstviye ustanavlivayetsya, chto syemyeistvo vsyekh ∑α-1-mnozhyestv imyeyet vychislimuyu pozitivnuyu nyerazryeshimuyu numyeratsiyu. Kromye togo, dlya kazhdogo ordinal'nogo oboznachyeniya a>1 stroitsya byeskonyechnoye syemyeistvo ∑α-1-mnozhyestv, obladayuscyeye vychislimoi pozitivnoi numyeratsiyei, no nye imyeyuscyei vychislimykh fridbyergovykh numyeratsii. EHto daet otvyet na vopros Badayeva-Goncharova o suscyestvovanii takikh syemyeistv na lyubom urovnye iyerarkhii YErshova (bud' to konyechnom ili byeskonyechnom), postavlyennyi imi tol'ko dlya konyechnykh urovnyei iyerarkhii YErshova vyshye urovnya 1

  79. Faizrakhmanov M.KH. T'yuringovyye skachki v iyerarkhii YErshova: avtoryef. dis. na soisk. uchyen. styep. kand. fiz.-mat. nauk: 01.01.06 / M.KH.Faizrakhmanov, Kazan. (Privolzh.) fyedyer. un-t, Kazan'. - Kazan', 2011. - 19 s.

  80. Faizrakhmanov M.KH. T'yuringovyye skachki v iyerarkhii YErshova / M.KH.Faizrakhmanov // Algyebra i logika. - 2011. - T.50, N 3. - S.399-414.
    Izuchayutsya byeskonyechnyye urovni iyerarkhii YErshova v yestyestvyennoi sistyemye oboznachyenii, yavlyayusciyesya sobstvyennymi dlya skachkov mnozhyestv. Dokazyvayetsya, chto sobstvyennymi byeskonyechnymi urovnyami dlya skachkov yavlyayutsya tol'ko urovni Δα-1, gdye α – oboznachyeniye dlya ordinala ωn > 1

  81. YUrii Lyeonidovich YErshov (k syemidyesyatilyetiyu so dnya rozhdyeniya) / A.A.Borovkov, S.K.Godunov, S.S.Goncharov, A.Konovalov, I.A.Lavrov, V.D.Mazurov, L.L.Maksimova, A.A.Mal'tsyev, B.G.Mikhailyenko, A.S.Morozov, A.A.Nikitin, YE.A.Palyutin, YU.G.Ryeshyetnyak // Uspyekhi matyematichyeskikh nauk. - 2011. - T.66, N 1. - S.201-204.

  82. Faizrakhmanov M.Kh. Turing jumps in the Ershov hierarchy / M.Kh.Faizrakhmanov // Algebra Logika. - 2011. - Vol.50, N 3. - P.279-289.
    We look at infinite levels of the Ershov hierarchy in the natural system of notation, which are proper for jumps of sets. It is proved that proper infinite levels for jumps are confined to Δα-1-levels, where α stands for an ordinal ωn > 1

  83. Leontieva M.N. Boolean algebras of elementary characteristic (1, 0, 1) whose set of atoms and Ershov–Tarski ideal are computable / M.N.Leontieva // Algebra Logika. - 2011. - Vol.50, N 2. - P.93-105.
    It is proved that there exists a computable Boolean algebra of elementary characteristics (1, 0, 1) which has a computable set of atoms and a computable Ershov–Tarski ideal, but no strongly computable isomorphic copy. Also a description of Δ60-computable Boolean algebras is presented.

  84. Yurij Leonidovich Ershov: (on his seventieth birthday) / A.A.ershov, S.K.Godunov, S.S.Goncharov, A.N.Konovalov, I.A.Lavrov, V.D.Mazurov, L.L.Maksimova, A.A.Mal'tsev, B.G.Mikhajlenko, A.S.Morozov, A.A.Nikitin, E.A.Palyutin, Yu.G.Reshetnyak // Russian Mathematical Surveys. - 2011. - Vol.66, N 1. - P.199-203.

  85. Arslanov M.M. Model-Theoretic Properties of Turing Degreesin the Ershov Difference Hierarchy / M.M.Arslanov // Proceedings of the Steklov Institute of Mathematics. - 2012. - Vol.278, Suppl.1. - P.S57–S65.

  86. Manat M. Positive undecidable numberings in the Ershov hierarchy / M.Manat, A.Sorbi // Algebra Logika. - 2012. - Vol.50, N 6. - P.512-525.
    A sufficient condition is given under which an infinite computable family of ∑α-1-sets has computable positive but undecidable numberings, where a is a notation for a nonzero computable ordinal. This extends a theorem proved for finite levels of the Ershov hierarchy in [1]. As a consequence, it is stated that the family of all ∑α-1-sets has a computable positive undecidable numbering. In addition, for every ordinal notation a>1, an infinite family of ∑α-1-sets is constructed which possesses a computable positive numbering but has no computable Friedberg numberings. This answers the question of whether such families exist at any - finite or infinite - level of the Ershov hierarchy, which was originally raised by Badaev and Goncharov only for the finite levels bigger than 1.

  87. Lauryeaty Dyemidovskoi pryemii 2013 goda // Nauka v Sibiri. - 2013. - N 45 (2930). - S.2.
    11 noyabrya v Pryezidiumye RAN sostoyalos' traditsionnoye chayepitiye, na kotorom byli nazvany imyena lauryeatov Dyemidovskoi pryemii 2013 goda. Imi stali akadyemiki YUrii Lyeonidovich YErshov, Alyeksandr Syergyeyevich Spirin i Klimyent Nikolayevich Trubyetskoi.

  88. Rassyel, Dzh. YErshov YUrii Lyeonidovich / Dzh. Rassyel. - M.: Kniga po Tryebovaniyu, 2013. - 100 s.

  89. Ospichev S.S. Properties of numberings in various levels of the Ershov hierarchy / S.S.Ospichev // Journal of Mathematical Sciences. - 2013. - Vol.188, N 4. - P.441-448.

  90. Akadyemik YU.L.YErshov: «Nado uchit' myslit' logichyeski» / YU.L.YErshov, byesyedu vyela O.Kolyesova // Nauka Urala. - 2014. - N 1/2.

  91. Nadtochii A. Vsye ostayetsya lyudyam / A.Nadtochii // Nauka v Sibiri. - 2014. - N 6 (2941). - S.3.
    V noyabrye 2013 goda odnim iz ochyeryednykh lauryeatov Dyemidovskoi pryemii stal akadyemik-matyematik YUrii Lyeonidovich YErshov. V kanun Dnya rossiiskoi nauki v YEkatyerinburgye sostoyalos' torzhyestvyennoye vruchyeniye ehtoi vyes'ma uvazhayemoi v nauchnom soobscyestvye nagrady.


Internet materials about life and work of academician Yu.L.Ershov
 
Schools of thought in NSC YU.L.YErshov | Index of worksPrepared by: V.Luk'yanova, I.Pavlova, S.Kann, N.SHtyrova  
  
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