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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The yellow cake


Authors: Andrzej Roslanowski and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 129 (2001), 279-291
MSC (2000): Primary 03E17, 03E35, 03E50
Published electronically: June 14, 2000
MathSciNet review: 1694876
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Abstract | References | Similar Articles | Additional Information

Abstract:

In this paper we consider the following property:

$(\circledast^{\mathrm{Da}})$ For every function $f:\mathbb{R}\times\mathbb{R}\longrightarrow\mathbb{R} $there are functions $g^0_n,g^1_n:\mathbb{R}\longrightarrow \mathbb{R} $

(for $n<\omega$) such that

\begin{displaymath}(\forall x,y\in\mathbb{R} )(f(x,y)=\sum_{n<\omega}g^0_n(x)g^1_n(y)).\end{displaymath}

We show that, despite some expectation suggested by S. Shelah (1997), $(\circledast^{\mathrm{Da}})$ does not imply $\mathbf{MA}(\sigma\mbox{-centered})$. Next, we introduce cardinal characteristics of the continuum responsible for the failure of $(\circledast^{\mathrm{Da}})$.


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Additional Information

Andrzej Roslanowski
Affiliation: Department of Mathematics and Computer Science, Boise State University, Boise, Idaho 83725 and Mathematical Institute of Wroclaw University, 50384 Wroclaw, Poland
Address at time of publication: Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska 68182
Email: roslanowski@unomaha.edu

Saharon Shelah
Affiliation: Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel, and Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
Email: shelah@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05538-6
PII: S 0002-9939(00)05538-6
Received by editor(s): September 25, 1998
Received by editor(s) in revised form: March 31, 1999
Published electronically: June 14, 2000
Additional Notes: The first author thanks the Hebrew University of Jerusalem for support during his visit to Jerusalem in Summer ’98 when most of this research was done and the KBN (Polish Committee of Scientific Research) for partial support through grant 2P03A03114.
The research of the second author was partially supported by The Israel Science Foundation. Publication 686.
Communicated by: Carl G. Jockusch
Article copyright: © Copyright 2000 American Mathematical Society