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The Lindenbaum-Tarski algebra for Boolean algebras with distinguished ideals

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Abstract

A complete solution is given to the problem of describing algebras with distinguished ideals, formulated by Peretyatkin. It is proven that such an algebra is isomorphic toℬ ωω× η, an interval algebra of the linear ordering ωω × η. I-algebras the elementary theory of each of which is axiomatizable by a single atom in some finite quotient with respect to the Frechet ideal of the Lindenbaum-Tarski algebra for the class of Boolean algebras with distinguished ideals are fully described in terms of direct summands.

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Authors
  1. D. E. Pal'chunov
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Additional information

Translated fromAlgebra i Logika, Vol. 34, No. 1, pp. 88–116, January–February, 1995.

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Pal'chunov, D.E. The Lindenbaum-Tarski algebra for Boolean algebras with distinguished ideals. Algebr Logic 34, 50–65 (1995). https://doi.org/10.1007/BF00750556

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  • DOI: https://doi.org/10.1007/BF00750556

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