TY - JOUR
T1 - The yellow cake
AU - Roslanowski, Andrzej
AU - Shelah, Saharon
PY - 2001
Y1 - 2001
N2 - In this paper we consider the following property: (Da) For every function / : ℝ × ℝ → ℝ there are functions gn0,gn1 : ℝ → ℝ (for n < ω) such that (∀x, y ∈ ℝ)(f(x, y) = ∑n<ω gn0(x)9n1(y)). We show that, despite some expectation suggested by S. Shelah (1997), (Da) does not imply MA(σ-centered). Next, we introduce cardinal characteristics of the continuum responsible for the failure of (Da).
AB - In this paper we consider the following property: (Da) For every function / : ℝ × ℝ → ℝ there are functions gn0,gn1 : ℝ → ℝ (for n < ω) such that (∀x, y ∈ ℝ)(f(x, y) = ∑n<ω gn0(x)9n1(y)). We show that, despite some expectation suggested by S. Shelah (1997), (Da) does not imply MA(σ-centered). Next, we introduce cardinal characteristics of the continuum responsible for the failure of (Da).
UR - http://www.scopus.com/inward/record.url?scp=23944450562&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-00-05538-6
DO - 10.1090/s0002-9939-00-05538-6
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AN - SCOPUS:23944450562
SN - 0002-9939
VL - 129
SP - 279
EP - 291
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 1
ER -