About: Quotients of Boolean algebras and regular subalgebras

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	Quotients of Boolean algebras and regular subalgebras Quotients of Boolean algebras and regular subalgebras (en)
skos:prefLabel	Quotients of Boolean algebras and regular subalgebras Quotients of Boolean algebras and regular subalgebras (en)
skos:notation	RIV/67985840:_____/10:00342828!RIV11-MSM-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190509), P(MEB060909), Z(AV0Z10190503), Z(AV0Z10750506), Z(MSM0021620845)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Balcar, Bohuslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	283710
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00342828
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Boolean algebra; sequential topology; ZFC extension; ideal (en)
http://linked.open.../riv/klicoveSlovo	Boolean algebra ideal ZFC extension sequential topology
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[A6D4F41F7A72]
http://linked.open...i/riv/nazevZdroje	Archive for Mathematical Logic
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Set theory and its applications Measure algebras
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	49
http://linked.open...iv/tvurceVysledku	Pazák, Tomáš Balcar, Bohuslav
http://linked.open...ain/vavai/riv/wos	000276360100004
http://linked.open...n/vavai/riv/zamer	Teoretický výzkum komplexních jevů ve fyzice, biologii a vědách o společnosti. Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	1432-0665
number of pages	14 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Quotients of Boolean algebras and regular subalgebras Quotients of Boolean algebras and regular subalgebras Quotients of Boolean algebras and regular subalgebras

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