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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F10%3A00342828%21RIV11-MSM-67985840
rdf:type
n5:Vysledek skos:Concept
dcterms: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 regular one, where U(Os)(B) is the Urysohn closure of the zero-convergence structure on B. 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.
dcterms:title
Quotients of Boolean algebras and regular subalgebras Quotients of Boolean algebras and regular subalgebras
skos:prefLabel
Quotients of Boolean algebras and regular subalgebras Quotients of Boolean algebras and regular subalgebras
skos:notation
RIV/67985840:_____/10:00342828!RIV11-MSM-67985840
n3:aktivita
n11:Z n11:P
n3:aktivity
P(IAA100190509), P(MEB060909), Z(AV0Z10190503), Z(AV0Z10750506), Z(MSM0021620845)
n3:cisloPeriodika
3
n3:dodaniDat
n10:2011
n3:domaciTvurceVysledku
n13:5794811
n3:druhVysledku
n15:J
n3:duvernostUdaju
n12:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
283710
n3:idVysledku
RIV/67985840:_____/10:00342828
n3:jazykVysledku
n4:eng
n3:klicovaSlova
Boolean algebra; sequential topology; ZFC extension; ideal
n3:klicoveSlovo
n7:sequential%20topology n7:ideal n7:Boolean%20algebra n7:ZFC%20extension
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[A6D4F41F7A72]
n3:nazevZdroje
Archive for Mathematical Logic
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n16:MEB060909 n16:IAA100190509
n3:rokUplatneniVysledku
n10:2010
n3:svazekPeriodika
49
n3:tvurceVysledku
Pazák, Tomáš Balcar, Bohuslav
n3:wos
000276360100004
n3:zamer
n8:MSM0021620845 n8:AV0Z10750506 n8:AV0Z10190503
s:issn
1432-0665
s:numberOfPages
14