Paper Info
Title
Finiteness conditions and distributive laws for Boolean algebras
Abstract
We compare diverse degrees of compactness and finiteness in Boolean algebras with each other and investigate the influence of weak choice principles. Our arguments rely on a discussion of infinitary distributive laws and generalized prime elements in Boolean algebras. In ZF set theory without choice, a Boolean algebra is Dedekind finite if and only if it satisfies the ascending chain condition. The Denumerable Subset Axiom (DS) implies finiteness of Boolean algebras with compact top, whereas the converse fails in ZF. Moreover, we derive from DS the atomicity of continuous Boolean algebras. Some of the results extend to more general structures like pseudocomplemented semilattices. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Year
DOI
Venue
2009
10.1002/malq.200810034
MATHEMATICAL LOGIC QUARTERLY
Keywords
Field
DocType
Atomistic lattice,Boolean algebra,chain condition,compact,continuous lattice,Dedekind finite,M-prime,M-distributive,pseudocomplemented
Interior algebra,Discrete mathematics,Stone's representation theorem for Boolean algebras,Combinatorics,Boolean algebras canonically defined,Parity function,Ideal (order theory),Law,Complete Boolean algebra,Two-element Boolean algebra,Mathematics,Free Boolean algebra
Journal
Volume
Issue
ISSN
55
6
0942-5616
Citations 
PageRank 
References 
1
0.63
3
Authors
1
Name
Order
Citations
PageRank
Marcel Erné12910.77