On well-splitting posets

Repovš, Dušan (author), Zdomskyy, Lyubomyr (author)

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.

• Language: English
• Keywords: splitting, bounding, Miller forcing, filter, Hurewicz space, mad family, Roitman problem
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2022
• Number of pages: Str. 995-1005
• Numbering: Vol. 61, iss. 7-8
• PID: 20.500.12556/RUL-142141
• UDC: 510.327:515.122
• ISSN on article: 0933-5846
• DOI: 10.1007/s00153-022-00818-6
• COBISS.SI-ID: 101041411
• Publication date in RUL: 21.10.2022

Record is a part of a journal

• Title: Archive for mathematical logic
• Shortened title: Arch. math. log.
• Publisher: Springer
• ISSN: 0933-5846
• COBISS.SI-ID: 3165967