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Free Boolean algebras over unions of two well orderings
- 1.0333038 - MÚ 2010 RIV NL eng J - Journal Article
Bonnet, R. - Faouzi, L. - Kubiś, Wieslaw
Free Boolean algebras over unions of two well orderings.
[Booleovské algebry nad sjednocením dvou dobrých uspořádání.]
Topology and its Applications. Roč. 156, č. 7 (2009), s. 1177-1185. ISSN 0166-8641. E-ISSN 1879-3207
Institutional research plan: CEZ:AV0Z10190503
Keywords : Well quasi orderings * Poset algebras * Superatomic Boolean algebras * Compact distributive lattices
Subject RIV: BA - General Mathematics
Impact factor: 0.441, year: 2009
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).
Je ukázáno, že pro každý nespočetný kardinál kapa existuje 2kapa navzájem neizomorfních volných Booleových algeber nad sjednocením dvou dobrých uspořádání mohutnosti <=kapa. To dává odpověď na otázku M. Pouzeta.
Permanent Link: http://hdl.handle.net/11104/0178123
Number of the records: 1