Computable Isomorphisms of Boolean Algebras with Operators

Studia Logica 100 (3):481-496 (2012)
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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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Tomasz Kowalski
La Trobe University

Citations of this work

Categoricity Spectra for Polymodal Algebras.Nikolay Bazhenov - 2016 - Studia Logica 104 (6):1083-1097.
Computable Heyting Algebras with Distinguished Atoms and Coatoms.Nikolay Bazhenov - 2023 - Journal of Logic, Language and Information 32 (1):3-18.

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References found in this work

Boolean Algebras with Operators.Alfred Tarski - 1953 - Journal of Symbolic Logic 18 (1):70-71.
Normal monomodal logics can simulate all others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.
Recursive isomorphism types of recursive Boolean algebras.J. B. Remmel - 1981 - Journal of Symbolic Logic 46 (3):572-594.
Normal Monomodal Logics Can Simulate All Others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.

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