D. E. Palchunov, A. V. Trofimov, “A superatomic Boolean algebra with a distinguished subalgebra whose theory lacks simple models”, Sibirsk. Mat. Zh., 2025, Volume 66, Number 3,Pages <nobr>506

A superatomic Boolean algebra with a distinguished subalgebra whose theory lacks simple models

D. E. Palchunov^a, A. V. Trofimov^b

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We construct a superatomic Boolean algebra with a distinguished subalgebra whose elementary theory lacks simple models.

Keywords: Boolean algebra, Boolean algebra with a distinguished subalgebra, local algebra, elementary theory, finitely axiomatizable theory, solvable theory, elementary equivalence.

UDC: 512.563

MSC: 35R30

Received: 12.09.2023
Revised: 21.02.2025
Accepted: 25.02.2025

DOI: 10.33048/smzh.2025.66.313