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
Full-text PDF Free Access
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
MR Author ID:
160185
ORCID:
0000-0003-0462-3152
Email:
shelah@math.huji.ac.il
Otmar Spinas
Affiliation:
Mathematik, ETH-Zentrum, 8092 ZΓΌrich, Switzerland
Email:
spinas@math.ethz.ch
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