TY - JOUR

T1 - Isomorphism of Atomless Boolean Algebras with Distinguished Ideals

AU - Goncharov, S. S.

AU - Xiang, J.

PY - 2025/4/29

Y1 - 2025/4/29

N2 - 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.

AB - 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.

KW - Boolean algebra with finitely many distinguished ideals (I-algebra)

KW - density of ideal

KW - isomorphism problem

KW - quotient algebra with respect to ideal

UR - https://www.mendeley.com/catalogue/56b0e800-581b-3d2b-b938-63f1716ef1a2/

U2 - 10.1007/s10469-025-09781-6

DO - 10.1007/s10469-025-09781-6

M3 - Article

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

ER -