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Algebra Logika, 2007, Volume 46, Number 6, Pages 729–744 (Mi al323)  

This article is cited in 13 scientific papers (total in 13 papers)

Spectra of degrees of some structures

I. Sh. Kalimullin

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: We argue for the existence of structures with the spectrum $\{\mathbf x:\mathbf x\not\le\mathbf a\}$ of degrees, where $\mathbf a$ is an arbitrary low degree. Also it is stated that there exist structures with the spectrum of degrees, $\{\mathbf x:\mathbf x\not\le\mathbf a\}\cup\{\mathbf x:\mathbf x\not\le\mathbf b\}$, for any low degrees $\mathbf a$ and $\mathbf b$.

Keywords: degrees of unsolvability, relative enumerability, presentations of structures, computable structures.

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English version:
Algebra and Logic, 2007, 46:6, 399–408

Bibliographic databases:

UDC: 510.53
Received: 12.12.2006

Citation: I. Sh. Kalimullin, “Spectra of degrees of some structures”, Algebra Logika, 46:6 (2007), 729–744; Algebra and Logic, 46:6 (2007), 399–408

Citation in format AMSBIB
\by I.~Sh.~Kalimullin
\paper Spectra of degrees of some structures
\jour Algebra Logika
\yr 2007
\vol 46
\issue 6
\pages 729--744
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 6
\pages 399--408

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. Sh. Kalimullin, “Restrictions on the degree spectra of algebraic structures”, Siberian Math. J., 49:6 (2008), 1034–1043  mathnet  crossref  mathscinet  isi
    2. Csima B.F., Kalimullin I.S., “Degree spectra and immunity properties”, MLQ Math. Log. Q., 56:1 (2010), 67–77  crossref  mathscinet  zmath  isi  scopus
    3. Frolov A. Kalimullin I. Harizanov V. Kudinov O. Miller R., “Spectra of High(N) and Non-Low(N) Degrees”, J. Logic Comput., 22:4, SI (2012), 755–777  crossref  mathscinet  zmath  isi  elib  scopus
    4. Kalimullin I., “Algorithmic Reducibilities of Algebraic Structures”, J. Logic Comput., 22:4, SI (2012), 831–843  crossref  mathscinet  zmath  isi  elib  scopus
    5. Fokina E.B. Harizanov V. Melnikov A., “Computable Model Theory”, Turing'S Legacy: Developments From Turing'S Ideas in Logic, Lecture Notes in Logic, 42, ed. Downey R., Cambridge Univ Press, 2014, 124–194  mathscinet  isi
    6. N. A. Bazhenov, “Boolean algebras with distinguished endomorphisms and generating trees”, J. Math. Sci., 215:4 (2016), 460–474  mathnet  crossref
    7. N. T. Kogabaev, “The theory of projective planes is complete with respect to degree spectra and effective dimensions”, Algebra and Logic, 54:5 (2015), 387–407  mathnet  crossref  crossref  mathscinet  isi
    8. N. T. Kogabaev, “Freely generated projective planes with finite computable dimension”, Algebra and Logic, 55:6 (2017), 461–484  mathnet  crossref  crossref  isi
    9. Andrews U., Cai M., Kalimullin I.Sh., Lempp S., Miller J.S., Montalban A., “the Complements of Lower Cones of Degrees and the Degree Spectra of Structures”, J. Symb. Log., 81:3 (2016), 997–1006  crossref  mathscinet  zmath  isi  scopus
    10. Andrews U., Cai M., Diamondstone D., Lempp S., Miller J.S., “Theory Spectra and Classes of Theories”, Trans. Am. Math. Soc., 369:9 (2017), 6493–6510  crossref  mathscinet  zmath  isi  scopus
    11. I. Sh. Kalimullin, M. Kh. Faizrakhmanov, “O stepenyakh perechislenii schetnykh semeistv vekhnerovskogo tipa”, Trudy seminara kafedry algebry i matematicheskoi logiki Kazanskogo (Privolzhskogo) federalnogo universiteta, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 157, VINITI RAN, M., 2018, 59–69  mathnet  mathscinet
    12. I. Sh. Kalimullin, V. L. Selivanov, A. N. Frolov, “Spektry stepenei struktur”, Trudy seminara kafedry algebry i matematicheskoi logiki Kazanskogo (Privolzhskogo) federalnogo universiteta, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 158, VINITI RAN, M., 2018, 23–39  mathnet  mathscinet
    13. Fokina E. Rossegger D. San Mauro L., “Bi-Embeddability Spectra and Bases of Spectra”, Math. Log. Q., 65:2 (2019), 228–236  crossref  mathscinet  zmath  isi  scopus
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