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Algebra Logika, 2008, Volume 47, Number 1, Pages 108–126 (Mi al349)  

This article is cited in 9 scientific papers (total in 9 papers)

Degrees of presentability of structures. II

A. I. Stukachev

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

Abstract: We show that the property of being locally constructivizable is inherited under Muchnik reducibility, which is weakest among the effective reducibilities considered over countable structures. It is stated that local constructivizability of level higher than 1 is inherited under $\Sigma$-reducibility but is not inherited under Medvedev reducibility. An example of a structure $\mathfrak M$ and a relation $P\subseteq M$ is constructed for which $\underline{(\mathfrak M,P)}\equiv\underline{\mathfrak M}$ but $(\mathfrak M,P)\not\equiv_\Sigma\mathfrak M$. Also, we point out a class of structures which are effectively defined by a family of their local theories.

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

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English version:
Algebra and Logic, 2008, 47:1, 65–74

Bibliographic databases:

UDC: 510.5
Received: 23.08.2006

Citation: A. I. Stukachev, “Degrees of presentability of structures. II”, Algebra Logika, 47:1 (2008), 108–126; Algebra and Logic, 47:1 (2008), 65–74

Citation in format AMSBIB
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\paper Degrees of presentability of structures.~II
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\pages 108--126
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\jour Algebra and Logic
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\vol 47
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\pages 65--74
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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. A. I. Stukachev, “Teorema ob obraschenii skachka dlya polureshetok $\Sigma$-stepenei”, Sib. elektron. matem. izv., 6 (2009), 182–190  mathnet  mathscinet
    2. A. I. Stukachev, “$\Sigma$-definability of uncountable models of $c$-simple theories”, Siberian Math. J., 51:3 (2010), 515–524  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. A. I. Stukachev, “Properties of $s\Sigma$-reducibility”, Algebra and Logic, 53:5 (2014), 405–417  mathnet  crossref  mathscinet  isi
    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. A. I. Stukachev, “Generalized hyperarithmetical computability over structures”, Algebra and Logic, 55:6 (2017), 507–526  mathnet  crossref  crossref  isi
    7. 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
    8. A. I. Stukachev, “Processes and structures on approximation spaces”, Algebra and Logic, 56:1 (2017), 63–74  mathnet  crossref  crossref  mathscinet  isi
    9. Dino Rossegger, “On functors enumerating structures”, Sib. elektron. matem. izv., 14 (2017), 690–702  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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