RT Journal Article
T1 An undecidable case of lineability in R-R
A1 Gámez Merino, José Luis
A1 Seoane-Sepúlveda, Juan B.
AB Recently, it has been proved that, assuming that there is an almost disjoint family of cardinality 2(c) in c (which is assured, for instance, by either Martin's Axiom, or the Continuum Hypothesis, or even 2(<c) = c) one has that the set of Sierpinski-Zygmund functions is 2(c)-strongly algebrable (and, thus, 2(c)-lineable). Here we prove that these two statements are actually equivalent and, moreover, that they both are undecidable. This would be the first time in which one encounters an undecidable proposition in the recently coined theory of lineability and spaceability.
PB Elsevier
SN 0022-247X
YR 2013
FD 2013-05-15
LK https://hdl.handle.net/20.500.14352/33279
UL https://hdl.handle.net/20.500.14352/33279
LA eng
NO Spanish Ministry of Science and Innovation
DS Docta Complutense
RD 28 abr 2024