Isomorphism of atomless Boolean algebras with distinguished ideal

S. S. Goncharov ; J. Xiang

Algebra i logika, Tome 63 (2024) no. 3, pp. 271-279

Résumé

An algebraic, model-theoretic, and algorithmic theory of enriched Boolean algebras with distinguished ideals was developed in a series of papers by D. E. Pal'chunov, A. Touraille, P. E. Alaev, N. T. Kogabaev, and other authors. Here we study the problem on the number of countable Boolean algebras with distinguished ideals for the case when an algebra and its quotient with respect to a distinguished ideal are atomless. It is proved that, for this subclass, there exist continuum many such countable structures.

Détail

Keywords: isomorphism problem, Boolean algebra with finitely many distinguished ideals (I-algebra), density of ideal, quotient algebra with respect to ideal.

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