About: Forcing properties of ideals of closed sets

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	With every sigma-ideal I on a Polish space we associate the sigma-ideal I* generated by the closed sets in I. We study the forcing notions of Borel sets modulo the respective sigma-ideals I and I* and find connections between their forcing properties. To this end, we associate to a sigma-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the ideal. We also study the I-I or constant property of sigma-ideals. i.e., the property that every Borel function defined on a Borel positive set can be restricted to a positive Borel set on which it either 1-1 or constant. We prove the following dichotomy: if I is a sigma-ideal generated by closed sets, then either the forcing P(I) adds a Cohen real, or else I has the 1-1 or constant property. With every sigma-ideal I on a Polish space we associate the sigma-ideal I* generated by the closed sets in I. We study the forcing notions of Borel sets modulo the respective sigma-ideals I and I* and find connections between their forcing properties. To this end, we associate to a sigma-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the ideal. We also study the I-I or constant property of sigma-ideals. i.e., the property that every Borel function defined on a Borel positive set can be restricted to a positive Borel set on which it either 1-1 or constant. We prove the following dichotomy: if I is a sigma-ideal generated by closed sets, then either the forcing P(I) adds a Cohen real, or else I has the 1-1 or constant property. (en)
Title	Forcing properties of ideals of closed sets Forcing properties of ideals of closed sets (en)
skos:prefLabel	Forcing properties of ideals of closed sets Forcing properties of ideals of closed sets (en)
skos:notation	RIV/67985840:_____/11:00371062!RIV12-AV0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100190902), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Zapletal, Jindřich
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	200095
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/11:00371062
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	forcing; ideals; Katetov order (en)
http://linked.open.../riv/klicoveSlovo	Katetov order forcing ideals
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[05F4C3CB2428]
http://linked.open...i/riv/nazevZdroje	Journal of Symbolic 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	Mathematical logic, complexity, and algorithms
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	76
http://linked.open...iv/tvurceVysledku	Sabok, M. Zapletal, Jindřich
http://linked.open...ain/vavai/riv/wos	000294791900017
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0022-4812
number of pages	21 (xsd:int)

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