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- W4320183019 abstract "Abstract We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are $${mathcal {B}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>B</mml:mi> </mml:math> -Canjar for any countably directed unbounded family $${mathcal {B}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>B</mml:mi> </mml:math> of the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that $${mathfrak {b}}=omega _1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> in every extension by the above forcing notions." @default.
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- W4320183019 date "2023-02-12" @default.
- W4320183019 modified "2023-10-18" @default.
- W4320183019 title "Towers, mad families, and unboundedness" @default.
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- W4320183019 doi "https://doi.org/10.1007/s00153-023-00861-x" @default.
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