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Quotients of Boolean algebras and regular subalgebras
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SYSNO ASEP 0342828 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Quotients of Boolean algebras and regular subalgebras Tvůrce(i) Balcar, Bohuslav (MU-W) RID, SAI
Pazák, Tomáš (UTIA-B)Zdroj.dok. Archive for Mathematical Logic. - : Springer - ISSN 0933-5846
Roč. 49, č. 3 (2010), s. 329-342Poč.str. 14 s. Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova Boolean algebra ; sequential topology ; ZFC extension ; ideal Vědní obor RIV BA - Obecná matematika CEP IAA100190509 GA AV ČR - Akademie věd MEB060909 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy CEZ AV0Z10190503 - MU-W (2005-2011) AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000276360100004 EID SCOPUS 77952097856 DOI 10.1007/s00153-010-0174-y Anotace 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 regular one, where U(Os)(B) is the Urysohn closure of the zero-convergence structure on B. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2011
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