The yellow cake

Andrzej Roslanowski; Saharon Shelah

doi:10.1090/s0002-9939-00-05538-6

The yellow cake

Andrzej Roslanowski^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we consider the following property: (^Da) For every function / : ℝ × ℝ → ℝ there are functions g_n⁰,g_n¹ : ℝ → ℝ (for n < ω) such that (∀x, y ∈ ℝ)(f(x, y) = _∑n<ω g_n⁰(x)9_n¹(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).

Original language	English
Pages (from-to)	279-291
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	129
Issue number	1
DOIs	https://doi.org/10.1090/s0002-9939-00-05538-6
State	Published - 2001

Access to Document

10.1090/s0002-9939-00-05538-6

Cite this

@article{b601d73d84f64bfdbcbfb020e02b7662,

title = "The yellow cake",

abstract = "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).",

author = "Andrzej Roslanowski and Saharon Shelah",

year = "2001",

doi = "10.1090/s0002-9939-00-05538-6",

language = "אנגלית",

volume = "129",

pages = "279--291",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}

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 - https://www.scopus.com/pages/publications/23944450562

U2 - 10.1090/s0002-9939-00-05538-6

DO - 10.1090/s0002-9939-00-05538-6

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -

The yellow cake

Abstract

Access to Document

Other files and links

Fingerprint

Cite this