Studia Logica

, Volume 100, Issue 3, pp 481–496

Computable Isomorphisms of Boolean Algebras with Operators

Article

DOI: 10.1007/s11225-012-9411-1

Cite this article as:
Khoussainov, B. & Kowalski, T. Stud Logica (2012) 100: 481. doi:10.1007/s11225-012-9411-1

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 isomorphismBoolean algebra with operatorsDegree spectrum

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceAuckland UniversityAucklandNew Zealand
  2. 2.Department of Mathematics and StatisticsLa Trobe UniversityBundooraAustralia