Free Boolean algebras over unions of two well orderings

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Free Boolean algebras over unions of two well orderings

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

Free Boolean algebras over unions of two well orderings

Popis výsledku anglicky

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).

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Topology and its Applications

ISSN

0166-8641

e-ISSN

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Svazek periodika

156

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

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Kód UT WoS článku

000264904500003

EID výsledku v databázi Scopus

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