Quotients of Boolean algebras and regular subalgebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00342828" target="_blank" >RIV/67985840:_____/10:00342828 - isvavai.cz</a>
Alternative codes found
RIV/67985556:_____/10:00342828 RIV/00216208:11620/10:10052089
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Quotients of Boolean algebras and regular subalgebras
Original language description
Let B and C be Boolean algebras and e : B -> C an embedding. We examine the hierarchy of ideals on C for which (e) over bar : B -> C/I is a regular (i.e. complete) embedding. As an application we deal with the interrelationship between P(omega)/fin in the ground model and in its extension. If M is an extension of V containing a new subset of omega, then in M there is an almost disjoint refinement of the family ([omega](omega))(V). Moreover, there is, in M, exactly one ideal I on omega such that (P(omega)/fin)(V) is a dense subalgebra of (P(omega)/I)(M) if and only if M does not contain an independent (splitting) real. We show that for a generic extension V[G], the canonical embedding P-V(omega)/fin hooked right arrow P(omega)/(U(Os)(B))(G) is a regularone, where U(Os)(B) is the Urysohn closure of the zero-convergence structure on B.
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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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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