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Computable Heyting Algebras with Distinguished Atoms and Coatoms

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Abstract

The paper studies Heyting algebras within the framework of computable structure theory. We prove that the class K containing all Heyting algebras with distinguished atoms and coatoms is complete in the sense of the work of Hirschfeldt et al. (Ann Pure Appl Logic 115(1-3):71-113, 2002). This shows that the class K is rich from the computability-theoretic point of view: for example, every possible degree spectrum can be realized by a countable structure from K. In addition, there is no simple syntactic characterization of computably categorical members of K (i.e., structures from K possessing a unique computable copy, up to computable isomorphisms).

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  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Nikolay Bazhenov

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  1. Nikolay Bazhenov
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Correspondence to Nikolay Bazhenov.

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The work was supported by the Ministry of Education and Science of the Republic of Kazakhstan, Grant AP08856493 “Positive graphs and computable reducibility on them as mathematical model of databases”. The author is also partially supported by RFBR, project number 20-31-70006.

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Bazhenov, N. Computable Heyting Algebras with Distinguished Atoms and Coatoms. J of Log Lang and Inf 32, 3–18 (2023). https://doi.org/10.1007/s10849-022-09371-0

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