## The yellow cake

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- by Andrzej Rosłanowski and Saharon Shelah PDF
- Proc. Amer. Math. Soc.
**129**(2001), 279-291 Request permission

## 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 \[ (\forall x,y\in \mathbb {R})(f(x,y)=\sum _{n<\omega }g^0_n(x)g^1_n(y)).\] 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 $(\circledast ^{\mathrm {Da}})$.## References

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## Additional Information

**Andrzej Rosłanowski**- 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
- MR Author ID: 288334
- 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
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**129**(2001), 279-291 - MSC (2000): Primary 03E17, 03E35, 03E50
- DOI: https://doi.org/10.1090/S0002-9939-00-05538-6
- MathSciNet review: 1694876