On well-splitting posets

Repovš, Dušan (avtor), Zdomskyy, Lyubomyr (avtor)

We introduce a class of proper posets which is preserved under countable support iterations, includes ▫$\omega^\omega$▫-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the property that the ground model reals remain splitting and unbounded in corresponding extensions. Our results may be considered as a possible path towards solving variations of the famous Roitman problem.

• Jezik: Angleški jezik
• Ključne besede: splitting, bounding, Miller forcing, filter, Hurewicz space, mad family, Roitman problem
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2022
• Št. strani: Str. 995-1005
• Številčenje: Vol. 61, iss. 7-8
• PID: 20.500.12556/RUL-142141
• UDK: 510.327:515.122
• ISSN pri članku: 0933-5846
• DOI: 10.1007/s00153-022-00818-6
• COBISS.SI-ID: 101041411
• Datum objave v RUL: 21.10.2022

Gradivo je del revije

• Naslov: Archive for mathematical logic
• Skrajšan naslov: Arch. math. log.
• Založnik: Springer
• ISSN: 0933-5846
• COBISS.SI-ID: 3165967