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Free Boolean algebras over unions of two well orderings
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SYSNO ASEP 0333038 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Free Boolean algebras over unions of two well orderings Title Booleovské algebry nad sjednocením dvou dobrých uspořádání Author(s) Bonnet, R. (FR)
Faouzi, L. (MA)
Kubiś, Wieslaw (MU-W) RID, ORCID, SAISource Title Topology and its Applications. - : Elsevier - ISSN 0166-8641
Roč. 156, č. 7 (2009), s. 1177-1185Number of pages 9 s. Language eng - English Country NL - Netherlands Keywords Well quasi orderings ; Poset algebras ; Superatomic Boolean algebras ; Compact distributive lattices Subject RIV BA - General Mathematics CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000264904500003 DOI 10.1016/j.topol.2008.12.01 Annotation Given a partially ordered set P there exists the most general Boolean algebra (F) over cap (P) which contains P as a generating set, called the free Boolean algebra over P. We study free Boolean algebras over posets of the form P = P-0 boolean OR P-1, where P-0, P-1 are well orderings. We call them nearly ordinal algebras. Answering a question of Maurice Pouzet, we show that for every uncountable cardinal kappa there are 2(kappa) pairwise non-isomorphic nearly ordinal algebras of cardinality kappa. Topologically, free Boolean algebras over posets correspond to compact 0-dimensional distributive lattices. In this context, we classify all closed sublattices of the product (omega(1) + 1) x (omega(1) + 1), showing that there are only N-1 many types. In contrast with the last result, we show that there are 2(N)1, topological types of closed subsets of the Tikhonov plank (omega(1) + 1) x (omega + 1). Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2010
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