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Free Boolean algebras over unions of two well orderings
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SYSNO ASEP 0333038 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Free Boolean algebras over unions of two well orderings Překlad názvu Booleovské algebry nad sjednocením dvou dobrých uspořádání Tvůrce(i) Bonnet, R. (FR)
Faouzi, L. (MA)
Kubiś, Wieslaw (MU-W) RID, ORCID, SAIZdroj.dok. Topology and its Applications. - : Elsevier - ISSN 0166-8641
Roč. 156, č. 7 (2009), s. 1177-1185Poč.str. 9 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova Well quasi orderings ; Poset algebras ; Superatomic Boolean algebras ; Compact distributive lattices Vědní obor RIV BA - Obecná matematika CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000264904500003 DOI 10.1016/j.topol.2008.12.01 Anotace 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). Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2010
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