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Algebra Logika, 2007, Volume 46, Number 6, Pages 763–788 (Mi al325)  

This article is cited in 16 scientific papers (total in 16 papers)

Degrees of presentability of structures. I

A. I. Stukachev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Presentations of structures in admissible sets, as well as different relations of effective reducibility between the structures, are treated. Semilattices of degrees of $\Sigma$-definability are the main object of investigation. It is shown that the semilattice of degrees of $\Sigma$-definability of countable structures agrees well with semilattices of $T$- and $e$-degrees of subsets of natural numbers. Also an attempt is made to study properties of the structures that are inherited under various effective reducibilities and explore how degrees of presentability depend on choices of different admissible sets as domains for presentations.

Keywords: admissible set, structure, semilattice of degrees of $\Sigma$-definability.

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English version:
Algebra and Logic, 2007, 46:6, 419–432

Bibliographic databases:

UDC: 510.5
Received: 14.11.2005
Revised: 12.03.2007

Citation: A. I. Stukachev, “Degrees of presentability of structures. I”, Algebra Logika, 46:6 (2007), 763–788; Algebra and Logic, 46:6 (2007), 419–432

Citation in format AMSBIB
\by A.~I.~Stukachev
\paper Degrees of presentability of structures.~I
\jour Algebra Logika
\yr 2007
\vol 46
\issue 6
\pages 763--788
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 6
\pages 419--432

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    This publication is cited in the following articles:
    1. A. I. Stukachev, “Degrees of presentability of structures. II”, Algebra and Logic, 47:1 (2008), 65–74  mathnet  crossref  mathscinet  zmath  isi
    2. I. Sh. Kalimullin, “Relations between algorithmic reducibilities of algebraic systems”, Russian Math. (Iz. VUZ), 53:6 (2009), 58–59  mathnet  crossref  mathscinet  zmath
    3. I. Sh. Kalimullin, “Uniform reducibility of representability problems for algebraic structures”, Siberian Math. J., 50:2 (2009), 265–271  mathnet  crossref  mathscinet  isi
    4. V. G. Puzarenko, “A certain reducibility on admissible sets”, Siberian Math. J., 50:2 (2009), 330–340  mathnet  crossref  mathscinet  isi
    5. A. I. Stukachev, “A jump inversion theorem for the semilattices of $\Sigma$-degrees”, Siberian Advances in Mathematics, 20:1 (2010), 68–74  mathnet  crossref  mathscinet
    6. V. G. Puzarenko, “Fixed points for the jump operator”, Algebra and Logic, 50:5 (2011), 418–438  mathnet  crossref  mathscinet  zmath  isi
    7. Kalimullin I., “Algorithmic Reducibilities of Algebraic Structures”, J. Logic Comput., 22:4, SI (2012), 831–843  crossref  mathscinet  zmath  isi  elib  scopus
    8. Montalban A., “Rice Sequences of Relations”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 370:1971, SI (2012), 3464–3487  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. A. I. Stukachev, “Properties of $s\Sigma$-reducibility”, Algebra and Logic, 53:5 (2014), 405–417  mathnet  crossref  mathscinet  isi
    10. 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
    11. A. I. Stukachev, “Generalized hyperarithmetical computability over structures”, Algebra and Logic, 55:6 (2017), 507–526  mathnet  crossref  crossref  isi
    12. Harrison-Trainor M., Melnikov A., Miller R., Montalban A., “Computable Functors and Effective Interpretability”, J. Symb. Log., 82:1 (2017), 77–97  crossref  mathscinet  zmath  isi  scopus
    13. A. I. Stukachev, “Processes and structures on approximation spaces”, Algebra and Logic, 56:1 (2017), 63–74  mathnet  crossref  crossref  mathscinet  isi
    14. Dino Rossegger, “On functors enumerating structures”, Sib. elektron. matem. izv., 14 (2017), 690–702  mathnet  crossref
    15. R. R. Avdeev, V. G. Puzarenko, “A computable structure with non-standard computability”, Siberian Adv. Math., 29:2 (2019), 77–115  mathnet  crossref  crossref
    16. A. S. Morozov, “$\Sigma$-preorderings in ${\mathbb{HF}(\mathbb{R})}$”, Algebra and Logic, 58:5 (2019), 405–416  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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