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arXiv · 1709.02326

Finding bases of uncountable free abelian groups is usually difficult

Noam Greenberg·Dan Turetsky·Linda Brown Westrick
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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.

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Noam Greenberg, Dan Turetsky, Linda Brown Westrick. 2017-09-07. Finding bases of uncountable free abelian groups is usually difficult. https://arxiv.org/abs/1709.02326

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