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An undecidable case of lineability in R-R

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Gámez Merino, José Luis and Seoane-Sepúlveda, Juan B. (2013) An undecidable case of lineability in R-R. Journal of Mathematical Analysis and Applications, 401 (2). pp. 959-962. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X12008918


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Lineability; Spaceability; Algebrability; Almost disjoint family; Sierpinski-Zygmund function; Erdos-Rado partition theorem
Subjects:Sciences > Mathematics > Algebra
ID Code:20645
Deposited On:04 Apr 2013 08:58
Last Modified:25 Nov 2016 12:28

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