The Yellow Cake

• Published in 1998
• Added on 2025-11-22

We consider the following property: (*) For every function \(f\) from \(\mathbb{R}^2 \to \mathbb{R}\) there are functions \(g_n, h_n\) from \(\mathbb{R}\) to \(\mathbb{R}\) (for \(n < \omega\)) such that for all real numbers \(x\) and \(y\), \(f(x,y) = \sum_{n<omega} g_n(x)h_n(y)\). We show that, despite some expectation suggested by [Sh:675], (*) does not imply MA(\(\sigma\)-centered). Next, we introduce cardinal characteristics of the continuum responsible for the failure of (*).

Links

• https://arxiv.org/abs/math/9810179v1
• https://arxiv.org/pdf/math/9810179v1

Other information

BibTeX entry

@article{TheYellowCake,
	key = {TheYellowCake},
	type = {article},
	title = {The Yellow Cake},
	author = {Andrzej Roslanowski and Saharon Shelah},
	abstract = {We consider the following property:
(*) For every function \(f\) from \(\mathbb{\{}R{\}}^2 \to \mathbb{\{}R{\}}\) there are functions \(g{\_}n, h{\_}n\) from \(\mathbb{\{}R{\}}\) to \(\mathbb{\{}R{\}}\) (for \(n < \omega\)) such that for all real numbers \(x\) and \(y\), \(f(x,y) = \sum{\_}{\{}n<omega{\}} g{\_}n(x)h{\_}n(y)\).
We show that, despite some expectation suggested by [Sh:675], (*) does not imply MA(\(\sigma\)-centered). Next, we introduce cardinal characteristics of the continuum responsible for the failure of (*).},
	comment = {},
	date_added = {2025-11-22},
	date_published = {1998-11-22},
	urls = {https://arxiv.org/abs/math/9810179v1,https://arxiv.org/pdf/math/9810179v1},
	collections = {food},
	url = {https://arxiv.org/abs/math/9810179v1 https://arxiv.org/pdf/math/9810179v1},
	year = 1998,
	urldate = {2025-11-22},
	archivePrefix = {arXiv},
	eprint = {math/9810179},
	primaryClass = {math.LO}
}