Počet záznamů: 1

Quotients of Boolean algebras and regular subalgebras

  1. 1.
    0342828 - MU-W 2011 RIV DE eng J - Článek v odborném periodiku
    Balcar, Bohuslav - Pazák, Tomáš
    Quotients of Boolean algebras and regular subalgebras.
    Archive for Mathematical Logic. Roč. 49, č. 3 (2010), s. 329-342 ISSN 1432-0665
    Grant CEP: GA AV ČR IAA100190509; GA MŠk MEB060909
    Výzkumný záměr: CEZ:AV0Z10190503; CEZ:AV0Z10750506
    Klíčová slova: Boolean algebra * sequential topology * ZFC extension * ideal
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.414, rok: 2010

    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.
    Trvalý link: http://hdl.handle.net/11104/0185452
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