Article

Studia Logica

, Volume 100, Issue 3, pp 481-496

Computable Isomorphisms of Boolean Algebras with Operators

  • Bakhadyr KhoussainovAffiliated withDepartment of Computer Science, Auckland University
  • , Tomasz KowalskiAffiliated withDepartment of Mathematics and Statistics, La Trobe University Email author 

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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.

Keywords

Computable isomorphism Boolean algebra with operators Degree spectrum