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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The distributivity numbers of $\mathcal{P}(\omega )$/fin
and its square


Authors: Saharon Shelah and Otmar Spinas
Journal: Trans. Amer. Math. Soc. 352 (2000), 2023-2047
MSC (1991): Primary 03E05, 06E05
DOI: https://doi.org/10.1090/S0002-9947-99-02270-9
Published electronically: April 13, 1999
MathSciNet review: 1751223
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Saharon Shelah
Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel
Email: shelah@math.huji.ac.il

Otmar Spinas
Affiliation: Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
Email: spinas@math.ethz.ch

DOI: https://doi.org/10.1090/S0002-9947-99-02270-9
Received by editor(s): February 12, 1997
Received by editor(s) in revised form: November 5, 1997
Published electronically: April 13, 1999
Additional Notes: The first author is supported by the Basic Research Foundation of the Israel Academy of Sciences; publication 494. The second author is supported by the Swiss National Science Foundation.
Article copyright: © Copyright 2000 American Mathematical Society