The distributivity numbers of 𝒫(𝜔)/fin and its square

Shelah, Saharon; Spinas, Otmar

doi:10.1090/S0002-9947-99-02270-9

The distributivity numbers of $\mathcal {P}(\omega )$/fin and its square
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by Saharon Shelah and Otmar Spinas

Trans. Amer. Math. Soc. 352 (2000), 2023-2047

DOI: https://doi.org/10.1090/S0002-9947-99-02270-9

Published electronically: April 13, 1999

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Abstract:

We show that in a model obtained by forcing with a countable support iteration of Mathias forcing of length $\omega _{2}$, the distributivity number of ${\mathcal {P}}(\omega )$/fin is $\omega _{2}$, whereas the distributivity number of r.o.$({\mathcal {P}}(\omega )$/fin)$^{2}$ is $\omega _{1}$. This answers a problem of Balcar, Pelant and Simon, and others.

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