Free Boolean algebras over unions of two well orderings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F09%3A00333038" target="_blank" >RIV/67985840:_____/09:00333038 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Free Boolean algebras over unions of two well orderings
Original language description
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).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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