Geodesic
Limitwise monotonic spectra of $\Sigma^0_2$-sets
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 107-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study classes of Turing degrees, contained in limitwise monotonic spectra. In particular, we prove that limitwise monotonic spectra of $\Sigma^0_2$-sets are co-meager. Moreover, we construct a $\Sigma^0_2$-set whose limitwise monotonic spectrum is co-null.
Keywords: computable functions, $\Sigma^0_2$-sets, limitwise monotonic functions, Turing degrees. 
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I. Sh. Kalimullin; M. Kh. Faizrakhmanov. Limitwise monotonic spectra of $\Sigma^0_2$-sets. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 2, pp. 107-116. http://geodesic.mathdoc.fr/item/UZKU_2012_154_2_a10/

[1] Downey R. G., Kach A. M., Turetsky D., “Limitwise monotonic functions and their applications”, Proceedings of the 11th Asian Logic Conference, World Sci. Publ., River Edge, N.J., 2011, 59–85 | MR

[2] Khoussainov B., Nies A., Shore R., “Computable models of theories with few models”, Notre Dame J. Formal Logic, 38:2 (1997), 165–178 | DOI | MR | Zbl

[3] Nies A., Computability and randomness, Oxford Univ. Press, N.Y., 2009, 420 pp. | MR | Zbl

[4] Jockusch C. G. (Jr.), Soare R. I., “$\Pi^0_1$-classes and degrees of theories”, Trans. Amer. Math. Soc., 173 (1972), 33–56 | MR | Zbl

[5] Wallbaum J., Computability of algebraic structures, Ph D Thesis, University of Notre Dame, Notre Dame, Indiana, 2010 | MR

[6] Kautz S. M., Degrees of Random Sets, Ph D Thesis, Cornell University, Ithaca, N.Y., 1991 | MR

[7] Kautz S. M., “An improved zero-one law for algorithmically random sequences”, Theor. Comput. Sci., 191:1–2 (1998), 185–192 | DOI | MR | Zbl

[8] Stillwell J., “Decidability of the “almost all” theory of degrees”, J. Symbolic Logic, 37:3 (1972), 501–506 | DOI | MR | Zbl

[9] Kechris A., Classical Descriptive Set Theory, Springer-Verlag, N.Y., 1995, 428 pp. | MR | Zbl

[10] Oxtoby J. C., Measure and Category: A Survey of the Analogies Between Topological and Measure Spaces, Springer-Verlag, N.Y., 1980, 124 pp. | MR | Zbl