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Osvaldo Guzmán, Michael Hrušák & Arturo Martínez-Celis

Notre Dame Journal of Formal Logic 58 (1):79-95 (2017)

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Analytic ideals and cofinal types.Alain Louveau & Boban Velickovi - 1999 - Annals of Pure and Applied Logic 99 (1-3):171-195.details We describe a new way to construct large subdirectly irreducibles within an equational class of algebras. We use this construction to show that there are forbidden geometries of multitraces for finite algebras in residually small equational classes. The construction is first applied to show that minimal equational classes generated by simple algebras of types 2, 3 or 4 are residually small if and only if they are congruence modular. As a second application of the construction we characterize residually small locally (...) Download Export citation Bookmark 9 citations
Analytic ideals and cofinal types.Alain Louveau & Boban Velickovi - 1999 - Annals of Pure and Applied Logic 99 (1-3):171-195.details Download Export citation Bookmark 10 citations
Mathias–Prikry and Laver–Prikry type forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.details We study the Mathias–Prikry and Laver–Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martinʼs number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias–Prikry forcing does not add a dominating real. Download Export citation Bookmark 13 citations
Forcing with filters and complete combinatorics.Claude Laflamme - 1989 - Annals of Pure and Applied Logic 42 (2):125-163.details We study ultrafilters produced by forcing, obtaining different combinatorics and related Rudin-Keisler ordering; in particular we answer a question of Baumgartner and Taylor regarding tensor products of ultrafilters. Adapting a method of Blass and Mathias, we show that in most cases the combinatorics satisfied by the ultrafilters recapture the forcing notion in the Lévy model. Download Export citation Bookmark 15 citations
Mob families and mad families.Jörg Brendle - 1998 - Archive for Mathematical Logic 37 (3):183-197.details We show the consistency of ${\frak o} <{\frak d}$ where ${\frak o}$ is the size of the smallest off-branch family, and ${\frak d}$ is as usual the dominating number. We also prove the consistency of ${\frak b} < {\frak a}$ with large continuum. Here, ${\frak b}$ is the unbounding number, and ${\frak a}$ is the almost disjointness number. Download Export citation Bookmark 16 citations
Mathias forcing and combinatorial covering properties of filters.David Chodounský, Dušan Repovš & Lyubomyr Zdomskyy - 2015 - Journal of Symbolic Logic 80 (4):1398-1410.details 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. Download Export citation Bookmark 13 citations

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