This is an announcement for the paper "An undecidable case of lineability in R^R" by Jose Luis Gamez-Merino and Juan B. Seoane-Sepulveda.

Abstract: Recently it has been proved that, assuming that there is an almost disjoint family of cardinality (2^{\mathfrak c}) in (\mathfrak c) (which is assured, for instance, by either Martin's Axiom, or CH, or even \mbox{$2^{<\mathfrak c}=\mathfrak c$}) one has that the set of Sierpi'nski-Zygmund functions is (2^{\mathfrak{c}})-strongly algebrable (and, thus, (2^{\mathfrak{c}})-lineable). Here we prove that these two statements are actually equivalent and, moreover, they both are undecidable. This would be the first time in which one encounters an undecidable proposition in the recently coined theory of lineability.

Archive classification: math.FA math.LO

Mathematics Subject Classification: 03E50, 03E75, 15A03, 26A15

Remarks: 5 pages

Submitted from: jseoane@mat.ucm.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.2906

or

http://arXiv.org/abs/1207.2906