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Computable Isomorphisms of Boolean Algebras with Operators

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Abstract

In this paper we investigate computable isomorphisms of Boolean algebras with operators (BAOs). We prove that there are examples of polymodal Boolean algebras with finitely many computable isomorphism types. We provide an example of a polymodal BAO such that it has exactly one computable isomorphism type but whose expansions by a constant have more than one computable isomorphism type. We also prove a general result showing that BAOs are complete with respect to the degree spectra of structures, computable dimensions, expansions by constants, and the degree spectra of relations.

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Authors and Affiliations

  1. Department of Computer Science, Auckland University, Auckland, New Zealand

    Bakhadyr Khoussainov

  2. Department of Mathematics and Statistics, La Trobe University, Bundoora, VIC, 3086, Australia

    Tomasz Kowalski

Authors
  1. Bakhadyr Khoussainov
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  2. Tomasz Kowalski
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Correspondence to Tomasz Kowalski.

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Khoussainov, B., Kowalski, T. Computable Isomorphisms of Boolean Algebras with Operators. Stud Logica 100, 481–496 (2012). https://doi.org/10.1007/s11225-012-9411-1

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  • DOI: https://doi.org/10.1007/s11225-012-9411-1

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