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2001 Pseudo Treealgebras
M. Bekkali
Notre Dame J. Formal Logic 42(2): 101-108 (2001). DOI: 10.1305/ndjfl/1054837936

Abstract

A pseudotree $ \langle T, \leq \rangle$ is a partially ordered set for which $ \{ u \in T: u \leq t \}$ is a linear ordering for each $ t \in T$. Define $ \mathcal{B}(T)$, the pseudo treealgebra over T, as the subalgebra of the power set of T generated by $ \{ b_{t} : t \in T \}$ where $ b_{t} = \{ u \in T : t \leq u \}$. It is shown that every pseudo treealgebra is embeddable into an interval algebra; thus it is a retractive Boolean algebra. Moreover, superatomicity of $ \mathcal{B}(T)$ is described using conditions on $ \langle T, \leq \rangle$.

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M. Bekkali. "Pseudo Treealgebras." Notre Dame J. Formal Logic 42 (2) 101 - 108, 2001. https://doi.org/10.1305/ndjfl/1054837936

Information

Published: 2001
First available in Project Euclid: 5 June 2003

zbMATH: 1032.06007
MathSciNet: MR1993393
Digital Object Identifier: 10.1305/ndjfl/1054837936

Subjects:
Primary: 03G , 06A
Secondary: 06A05, , 06B10 , 06E05

Keywords: interval algebra , ordered set , pseudo treealgebra

Rights: Copyright © 2001 University of Notre Dame

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