Journal of Symbolic Logic 80 (4):1398-1410 (2015)

Abstract
We give topological characterizations of filters${\cal F}$onωsuch 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.
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DOI 10.1017/jsl.2014.73
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References found in this work BETA

Mathias–Prikry and Laver–Prikry Type Forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.
Near Coherence of Filters. I. Cofinal Equivalence of Models of Arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
Forcing with Filters and Complete Combinatorics.Claude Laflamme - 1989 - Annals of Pure and Applied Logic 42 (2):125-163.
Cofinalities of Countable Ultraproducts: The Existence Theorem.R. Michael Canjar - 1989 - Notre Dame Journal of Formal Logic 30 (4):539-542.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.

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Citations of this work BETA

Products of Hurewicz Spaces in the Laver Model.Dušan Repovš & Lyubomyr Zdomskyy - 2017 - Bulletin of Symbolic Logic 23 (3):324-333.
Covering properties of $$omega $$ω -mad families.Leandro Aurichi & Lyubomyr Zdomskyy - 2020 - Archive for Mathematical Logic 59 (3):445-452.
Products of Menger Spaces: A Combinatorial Approach.Piotr Szewczak & Boaz Tsaban - 2017 - Annals of Pure and Applied Logic 168 (1):1-18.
Menger Remainders of Topological Groups.Angelo Bella, Seçil Tokgöz & Lyubomyr Zdomskyy - 2016 - Archive for Mathematical Logic 55 (5-6):767-784.

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