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Keeping additivity of the null ideal small


Author: Jindrich Zapletal
Journal: Proc. Amer. Math. Soc. 125 (1997), 2443-2451
MSC (1991): Primary 03E35, 03E50
DOI: https://doi.org/10.1090/S0002-9939-97-03870-7
MathSciNet review: 1389541
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Abstract: We shall show that various statements are consistent with additivity of the null ideal equal to $\aleph _{1};$ for example, ``all branchless trees of size $\aleph _{1}$ are special'', (S) conjecture and ``there are only five cofinal types of directed posets of size $\aleph _{1}$''.


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Additional Information

Jindrich Zapletal
Affiliation: M. S. R. I., 1000 Centennial Drive, Berkeley, California 94720
Address at time of publication: Mailcode 253-37, California Institute of Technology, Pasadena, California 91125
Email: jindra@msri.org, jindra@cco.caltech.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03870-7
Received by editor(s): November 8, 1995
Received by editor(s) in revised form: February 26, 1996
Additional Notes: Research at MSRI partially supported by NSF grant # DMS 9022140. The author wishes to thank Itay Neeman for asking the original inspiring question.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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