The Theories of Superatomic Boolean Algebras with Distinguished Subalgebra Which Lack Countably Saturated Models

D. E. Palchunov, A. V. Trofimov

Research output: Contribution to journalArticlepeer-review

Abstract

Studying Boolean algebras with distinguished subalgebras, we establish the existence of continuum many simple superatomic Boolean algebras with distinguished subalgebra whose elementary theories are distinct and each of them lacks countably saturated models. The subalgebras coincide with the Boolean algebras modulo their Fréchet ideals.

Original languageEnglish
Pages (from-to)516-527
Number of pages12
JournalSiberian Mathematical Journal
Volume61
Issue number3
DOIs
Publication statusPublished - 1 May 2020

Keywords

  • Boolean algebra
  • Boolean algebra with distinguished subalgebra
  • elementary equivalence
  • elementary theory
  • finitely axiomatizable theory
  • local algebra
  • solvable theory

Fingerprint Dive into the research topics of 'The Theories of Superatomic Boolean Algebras with Distinguished Subalgebra Which Lack Countably Saturated Models'. Together they form a unique fingerprint.

Cite this