Geodesic
On $\Delta^0_2$-Categoricity of Boolean Algebras
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 3-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the notions of $\Delta^0_2$-categoricity and relative $\Delta^0_2$-categoricity in Boolean algebras coincide. As a corollary, we obtain that for every Turing degree $\mathbf{d}\mathbf{0}'$ a computable Boolean algebra is $\mathbf{d}$-computably categorical if and only if it is computably categorical.
Keywords: Boolean algebra, $\Delta^{0}_{2}$-categoricity, computable categoricity. 
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N. A. Bazhenov. On $\Delta^0_2$-Categoricity of Boolean Algebras. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 3-14. http://geodesic.mathdoc.fr/item/VNGU_2013_13_2_a0/

[1] Fröhlich A., Shepherdson J., “Effective Procedures in Field Theory”, Philos. Trans. Roy. Soc. London. Ser. A, 248:950 (1956), 407–432 | DOI | MR | Zbl

[2] Maltsev A. I., “Konstruktivnye algebry, I”, Usp. mat. nauk, 16:3 (1961), 3–60 | MR

[3] Goncharov S. S., Ershov Yu. L., Konstruktivnye modeli, Nauch. kn., Novosibirsk, 1999

[4] Goncharov S. S., “Computability and Computable Models”, Mathematical Problems from Applied Logic II, eds. D. M. Gabbay, S. S. Goncharov, M. Zakharyaschev, Springer, N. Y., 2006, 99–216 | MR

[5] Goncharov S., Khoussainov B., “Open Problems in the Theory of Constructive Algebraic Systems”, Computability Theory and its Applications, eds. P. A. Cholak, S. Lempp, M. Lerman, R. A. Shore, Am. Math. Soc., Providence, 2000, 145–170 | DOI | MR | Zbl

[6] Goncharov S. S., “O chisle neavtoekvivalentnykh konstruktivizatsii”, Algebra i logika, 16:3 (1977), 257–282 | MR | Zbl

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

[8] Chisholm J., Fokina E. B., Goncharov S. S., Harizanov V. S., Knight J. F., Quinn S., “Intrinsic Bounds on Complexity and Definability at Limit Levels”, J. Symb. Logic, 74:3 (2009), 1047–1060 | DOI | MR | Zbl

[9] Goncharov S. S., “Avtoustoichivost i vychislimye semeistva konstruktivizatsii”, Algebra i logika, 14:6 (1975), 647–680 | MR | Zbl

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

[11] Remmel J. B., “Recursive Isomorphism Types of Recursive Boolean Algebras”, J. Symb. Logic, 46:3 (1981), 572–594 | DOI | MR | Zbl

[12] McCoy C., “$\Delta^0_2$-Categoricity in Boolean Algebras and Linear Orderings”, Ann. Pure Appl. Logic, 119:1–3 (2003), 85–120 | DOI | MR | Zbl

[13] Mak-Koi Ch. F. D., “O $\Delta^0_3$-kategorichnosti dlya lineinykh poryadkov i bulevykh algebr”, Algebra i logika, 41:5 (2002), 531–552 | MR

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

[15] Bazhenov N. A., “O kategorichnosti bulevykh algebr tipa $\mathfrak{B}(\omega^{\alpha}\times \eta)$ v giperarifmeticheskoi ierarkhii”, Vestn. Novosib. gos. un-ta. Seriya: Matematika, mekhanika, informatika, 12:3 (2012), 35–45

[16] Goncharov S. S., Schetnye bulevy algebry i razreshimost, Nauch. kn., Novosibirsk, 1996 | MR

[17] Soar R. I., Vychislimo perechislimye mnozhestva i stepeni, Kazanskoe matem. ob-vo, Kazan, 2000 | MR | Zbl

[18] Ash C. J., Khight J. F., Computable Structures and the Hyperarithmetical Hierarchy, Elsevier Science, Amsterdam, 2000 | Zbl

[19] Montalbán A., “On the Triple Jump of the Set of Atoms of a Boolean Algebra”, Proc. Amer. Math. Soc., 136:7 (2008), 2589–2595 | DOI | MR | Zbl

[20] Sacks G. E., “Recursive Enumerability and the Jump Operator”, Trans. Amer. Math. Soc., 108:2 (1963), 223–239 | DOI | MR | Zbl

[21] Goncharov S. S., “Nekotorye svoistva konstruktivizatsii bulevykh algebr”, Sib. mat. zhurn., 16:2 (1975), 264–278 | Zbl