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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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


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 $(\circledast ^{\mathrm {Da}})$.
  • Tomek Bartoszyński and Haim Judah, Set theory, A K Peters, Ltd., Wellesley, MA, 1995. On the structure of the real line. MR 1350295
  • Krzysztof Ciesielski. Set theoretic real analysis. Journal of Applied Analysis, 3:143-190, 1997.
  • Roy O. Davies, Representation of functions of two variables as sums of rectangular functions. I, Fund. Math. 85 (1974), no. 2, 177–183. MR 346108, DOI 10.4064/fm-85-2-177-183
  • Kenneth Kunen. Inaccessibility properties of cardinals. PhD thesis, Stanford University, 1968.
  • Arnold W. Miller, Arnie Miller’s problem list, Set theory of the reals (Ramat Gan, 1991) Israel Math. Conf. Proc., vol. 6, Bar-Ilan Univ., Ramat Gan, 1993, pp. 645–654. MR 1234292
  • Arnold W. Miller. Some interesting problems. Circulated notes; available at
  • Saharon Shelah. Whitehead groups may not be free, even assuming CH. II. Israel Journal of Mathematics, 35:257-285, 1980 .
  • Saharon Shelah, Cardinal arithmetic, Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR 1318912
  • Saharon Shelah. On Ciesielski’s Problems. Journal of Applied Analysis, 3(2):191-209, 1997.
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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:
  • 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:
  • 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:
  • MathSciNet review: 1694876