0342828 20240103193501.820101209235959.9 000276360100004 77952097856 10.1007/s00153-010-0174-y 14 s. cav_un_epca*02561860933-5846493 (2010)329-342Springer Boolean algebra sequential topology ZFC extension ideal cav_un_auth*0100647 Balcar Bohuslav Matematická logika a teoretická informatika Mathematical Logic and Theoretical Computer Science MLTCS MU-W Mathematical Logic and Theoretical Computer Science Matematický ústav AV ČR, v. v. i. cav_un_auth*0214086 Pazák Tomáš Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. http://link.springer.com/article/10.1007%2Fs00153-010-0174-y IAA100190509 GA AV ČR cav_un_auth*0000975 MEB060909 GA MŠk cav_un_auth*0252862 CEZ:AV0Z10190503 CEZ:AV0Z10750506 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. 2011 BA 4 R 4r 20231122134022.7 http://hdl.handle.net/11104/0185452 0.425 0.550 Q1 25.124 Q3 Q1 2010 Soubory v repozitáři: Balcar.pdf 77952097856 SCOPUS 000276360100004 WOS cav_un_epca*0256186 Archive for Mathematical Logic 0933-5846 1432-0665 Roč. 49 č. 3 2010 329 342 Springer