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MATHIAS FORCING AND COMBINATORIAL COVERING PROPERTIES OF FILTERS

Published online by Cambridge University Press:  22 December 2015

DAVID CHODOUNSKÝ
Affiliation:
INSTITUTE OF MATHEMATICS OF THE ACADEMY OF SCIENCES OF THE CZECH REPUBLIC ŽITNÁ 25 PRAHA 1, CZECH REPUBLICE-mail: david.chodounsky@matfyz.cz
DUŠAN REPOVŠ
Affiliation:
FACULTY OF EDUCATION AND FACULTY OF MATHEMATICS AND PHYSICS UNIVERSITY OF LJUBLJANA P. O. BOX 2964, LJUBLJANA 1001 SLOVENIAE-mail: dusan.repovs@guest.arnes.siURL: http://www.fmf.uni-lj.si/∼repovs/index.htm
LYUBOMYR ZDOMSKYY
Affiliation:
KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC UNIVERSITY OF VIENNA WÄHRINGER STRASSE 25 A-1090 WIEN, AUSTRIAE-mail: lzdomsky@gmail.comURL: http://www.logic.univie.ac.at/∼lzdomsky/

Abstract

We give topological characterizations of filters ${\cal F}$ on ω such that the Mathias forcing ${M_{\cal F}}$ 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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2015 

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