. . "Quotients of Boolean algebras and regular subalgebras" . "49" . "P(IAA100190509), P(MEB060909), Z(AV0Z10190503), Z(AV0Z10750506), Z(MSM0021620845)" . . . "RIV/67985840:_____/10:00342828" . "Quotients of Boolean algebras and regular subalgebras"@en . . "DE - Spolkov\u00E1 republika N\u011Bmecko" . "Boolean algebra; sequential topology; ZFC extension; ideal"@en . . . "3" . "Archive for Mathematical Logic" . "Quotients of Boolean algebras and regular subalgebras" . . "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 . . . . . . "2"^^ . "1432-0665" . "Paz\u00E1k, Tom\u00E1\u0161" . "283710" . "RIV/67985840:_____/10:00342828!RIV11-MSM-67985840" . . "1"^^ . "[A6D4F41F7A72]" . . "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." . . "Balcar, Bohuslav" . . . . . "Quotients of Boolean algebras and regular subalgebras"@en . "14"^^ . . "000276360100004" .