@article{63c3d0277e5c4ba5800f8f52a60ab405,
title = "Finding bases of uncountable free Abelian groups is usually difficult",
abstract = "We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show, under the assumption V = L, that there is a first-order definable free abelian group with no first-order definable basis.",
author = "Noam Greenberg and Dan Turetsky and Westrick, {Linda Brown}",
note = "Funding Information: Received by the editors January 23, 2016, and, in revised form, March 7, 2017. 2010 Mathematics Subject Classification. Primary 03C57; Secondary 03D60. The first author was supported by the Marsden Fund, a Rutherford Discovery Fellowship from the Royal Society of New Zealand, and by the Templeton Foundation via the Turing centenary project “Mind, Mechanism and Mathematics”. The third author was supported by the Rutherford Discovery Fellowship as a postdoctoral fellow. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",
year = "2018",
doi = "10.1090/tran/7232",
language = "English (US)",
volume = "370",
pages = "4483--4508",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "6",
}