On tree ideals

Goldstern, Martin; Repický, Miroslav; Shelah, Saharon; Spinas, Otmar

doi:10.1090/S0002-9939-1995-1233972-4

On tree ideals
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by Martin Goldstern, Miroslav Repický, Saharon Shelah and Otmar Spinas

Proc. Amer. Math. Soc. 123 (1995), 1573-1581

DOI: https://doi.org/10.1090/S0002-9939-1995-1233972-4

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Abstract:

Let ${l^0}$ and ${m^0}$ be the ideals associated with Laver and Miller forcing, respectively. We show that ${\mathbf {add}}({l^0}) < {\mathbf {cov}}({l^0})$ and ${\mathbf {add}}({m^0}) < {\mathbf {cov}}({m^0})$ are consistent. We also show that both Laver and Miller forcing collapse the continuum to a cardinal $\leq \mathfrak {h}$.

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