An undecidable case of lineability in R^R

By José L. Gámez-Merino, J. B. Seoane-Sep'ulveda. 2012

55 citations recorded by the source corpus.

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 $2^{<\mathfrak c=\mathfrak c$}) 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/11dd7b4055eff5f7829d98b3492371264eb731b3

How researchers see this paper

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In Applied Mathematics

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda

In Mathematical Physics

1. Daniel Pellegrino
2. L. González
3. J. Sepúlveda

Citations in the corpus

• Linear subsets of nonlinear sets in topological vector spaces (2013, methodology): “13 (Gámez-Merino and Seoane-Sepúlveda 2012 [152]).”