Geodesic
Degrees of categoricity for superatomic Boolean algebras
Algebra i logika, Tome 52 (2013) no. 3, pp. 271-283.

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It is proved that every computable superatomic Boolean algebra has a strong degree of categoricity.
Keywords: superatomic Boolean algebras, computable categoricity, degree of categoricity. 
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N. A. Bazhenov. Degrees of categoricity for superatomic Boolean algebras. Algebra i logika, Tome 52 (2013) no. 3, pp. 271-283. http://geodesic.mathdoc.fr/item/AL_2013_52_3_a0/

[1] S. Goncharov, V. Harizanov, J. Knight, C. McCoy, R. Miller, R. Solomon, “Enumerations in computable structure theory”, Ann. Pure Appl. Logic, 136:3 (2005), 219–246 | DOI | MR | Zbl

[2] J. Chisholm, E. B. Fokina, S. S. Goncharov, V. S. Harizanov, J. F. Knight, S. Quinn, “Intrinsic bounds on complexity and definability at limit levels”, J. Symb. Log., 74:3 (2009), 1047–1060 | DOI | MR | Zbl

[3] E. B. Fokina, I. Kalimullin, R. Miller, “Degrees of categoricity of computable structures”, Arch. Math. Logic, 49:1 (2010), 51–67 | DOI | MR | Zbl

[4] B. F. Csima, J. N. Y. Franklin, R. A. Shore, “Degrees of categoricity and the hyperarithmetic hierarchy”, Notre Dame J. Formal Logic, 54:2 (2013), 215–231 | DOI | MR | Zbl

[5] S. S. Goncharov, “Stepeni avtoustoichivosti otnositelno silnykh konstruktivizatsii”, Algoritmicheskie voprosy algebry i logiki, Csb. statei. K 80-letiyu so dnya rozhd. akad. S. I. Adyana, Tr. MIAN, 274, MAIK, M., 2011, 119–129 | MR

[6] S. S. Goncharov, V. D. Dzgoev, “Avtoustoichivost modelei”, Algebra i logika, 19:1 (1980), 45–58 | MR | Zbl

[7] J. B. Remmel, “Recursive isomorphism types of recursive Boolean algebras”, J. Symb. Log., 46:3 (1981), 572–594 | DOI | MR | Zbl

[8] C. McCoy, “$\Delta_2^0$-categoricity in Boolean algebras and linear orderings”, Ann. Pure Appl. Logic, 119:1–3 (2003), 85–120 | DOI | MR | Zbl

[9] Ch. F. D. Mak-Koi, “O $\Delta_3^0$-kategorichnosti dlya lineinykh poryadkov i bulevykh algebr”, Algebra i logika, 41:5 (2002), 531–552 | MR | Zbl

[10] K. Harris, Categoricity in Boolean algebras (to appear)

[11] N. A. Bazhenov, “O $\Delta_2^0$-kategorichnosti bulevykh algebr”, Vestnik NGU, Ser. matem., mekh., inform., 13:2 (2013), 3–14

[12] S. S. Goncharov, Schetnye bulevy algebry i razreshimost, Sibirskaya shkola algebry i logiki, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1996 | MR | Zbl

[13] S. S. Goncharov, Yu. L. Ershov, Konstruktivnye modeli, Sibirskaya shkola algebry i logiki, Nauchnaya kniga, Novosibirsk, 1999

[14] C. J. Ash, J. F. Knight, Computable structures and the hyperarithmetical hierarchy, Stud. Logic Found. Math., 144, Elsevier Sci. B.V., Amsterdam etc., 2000 | MR | Zbl

[15] Kh. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR

[16] S. S. Goncharov, “Konstruktiviziruemost superatomnykh bulevykh algebr”, Algebra i logika, 12:1 (1973), 31–40 | Zbl

[17] C. J. Ash, “Categoricity in hyperarithmetical degrees”, Ann. Pure Appl. Logic, 34:1 (1987), 1–14 | DOI | MR | Zbl

[18] P. M. Semukhin, “Spektry stepenei opredelimykh otnoshenii na bulevykh algebrakh”, Sib. matem. zh., 46:4 (2005), 928–941 | MR | Zbl