Abstract
We construct a model in which there exists a refining matrix of regular height λ larger than \(\mathfrak{h}\); both \(\lambda = \mathfrak{c}\) and \(\lambda < \mathfrak{c}\) are possible. A refining matrix is a refining system of mad families without common refinement. Of particular interest in our proof is the preservation of \({\cal B}\)-Canjarness.
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Acknowledgment
We want to thank Osvaldo Guzmán for his inspiring tutorial at the Winter School 2020 in Hejnice and for helpful discussion about \({\cal B}\)-Canjar filters, as well as to the anonymous referee for very many comments and suggestions, which significantly improved the quality of the manuscript.
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The authors would like to thank the Austrian Science Fund (FWF) for the generous support through grants Y1012, I4039 (Fischer, Wohofsky) and P28420 (Koelbing). The second author is also grateful for the support by the ÖAW Doc fellowship.
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Fischer, V., Koelbing, M. & Wohofsky, W. Refining systems of mad families. Isr. J. Math. (2024). https://doi.org/10.1007/s11856-024-2626-9
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DOI: https://doi.org/10.1007/s11856-024-2626-9