TY - JOUR

T1 - Elementary Equivalence of Countable Atomless Boolean Algebras with Distinguished Ideal

AU - Сян, Цзинхао

N1 - Xiang, J. Elementary Equivalence of Countable Atomless Boolean Algebras with Distinguished Ideal. Algebra Logic 64, 210–218 (2025). The research of the author was supported by a grant from the Russian Science Foundation No. 23-11-00170, https://rscf.ru/project/23-11-00170/ and partially by China Scholarship Council, https://www.csc.edu.cn.

PY - 2025/7

Y1 - 2025/7

N2 - We study the problem of elementary equivalence of countable atomless Boolean algebras with a distinguished nonprincipal and nondense ideal, constructed from different elementarily equivalent countable infinite atomic Boolean algebras, under the condition that both algebra and its quotient algebra by the given ideal are atomless. We prove the existence of a continuum family of such countable Boolean algebras with a distinguished ideal.

AB - We study the problem of elementary equivalence of countable atomless Boolean algebras with a distinguished nonprincipal and nondense ideal, constructed from different elementarily equivalent countable infinite atomic Boolean algebras, under the condition that both algebra and its quotient algebra by the given ideal are atomless. We prove the existence of a continuum family of such countable Boolean algebras with a distinguished ideal.

KW - isomorphism problem

KW - elementary equivalence problem

KW - Boolean algebra

KW - I-algebra

KW - density of ideal

UR - https://www.scopus.com/pages/publications/105033491520

U2 - 10.1007/s10469-026-09826-4

DO - 10.1007/s10469-026-09826-4

M3 - Article

VL - 64

SP - 210

EP - 218

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -