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Degrees of presentability of structures. II

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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 Σ-reducibility but is not inherited under Medvedev reducibility. An example of a structure \(\mathfrak{M}\) and a relation P ⊆ M is constructed for which \({\underline {({\mathfrak{M}},P)}} \equiv {\underline {\mathfrak{M}}} \) but \((\mathfrak{M},P)\) ≢∑ \(\mathfrak{M}\). Also, we point out a class of structures which are effectively defined by a family of their local theories.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    A. I. Stukachev

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  1. A. I. Stukachev
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Correspondence to A. I. Stukachev.

Additional information

Supported by RFBR (grant Nos. 05-0100481 and 06-0104002), by the Council for Grants (under RF President) for State Support of Young Candidates of Science and Their Supervisors (project MK-1239.2005.1), and by INTAS (project YSF 04-83-3310).

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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 108–126, January–February, 2008.

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Stukachev, A.I. Degrees of presentability of structures. II. Algebra Logic 47, 65–74 (2008). https://doi.org/10.1007/s10469-008-0007-9

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  • DOI: https://doi.org/10.1007/s10469-008-0007-9

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