Mathias forcing and combinatorial covering properties of filters

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

We give topological characterizations of filters ▫$\mathcal{F}$▫ on ▫$w$▫ such that the Mathias forcing ▫$M_\mathcal{F}$▫ adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Martínez, Minami, and Tsaban.

• Language: English
• Keywords: mathematics, topology, Menger space, Hurewicz space, $\gamma$-space, filter, ideal, Mathias forcing
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2015
• Number of pages: Str. 1398-1410
• Numbering: Vol. 80, no. 4
• PID: 20.500.12556/RUL-111421
• UDC: 515.122:510.3
• ISSN on article: 0022-4812
• DOI: http://dx.doi.org/10.1017/jsl.2014.73
• COBISS.SI-ID: 17556057
• Publication date in RUL: 30.09.2019

Record is a part of a journal

• Title: Journal of symbolic logic
• Shortened title: J. symb. log.
• Publisher: Association for Symbolic Logic.
• ISSN: 0022-4812
• COBISS.SI-ID: 25795584

Secondary language

• Language: Slovenian
• Keywords: matematika, topologija, topološki prostori, filter, ideal