Abstract
Whitehead’s Problem asks whether every Whitehead group is a free abelian group. Stein in 1951 showed that every countable Whitehead group is a free abelian group, but Shelah in 1974 showed that Whitehead’s Problem in general is independent of ZFC. In this paper, we study Whitehead’s Problem in reverse mathematics and, in particular, the proof-theoretic strength of Stein’s Theorem. We establish that over the base theory WKL0, ACA0 is equivalent to Stein’s Theorem, whereas over the base theory RCA0, WKL0 and Stein’s Theorem are incomparable; this is done by showing that Stein’s Theorem is true in REC.
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Sen, Y. Whitehead’s problem and reverse mathematics. Isr. J. Math. 228, 455–512 (2018). https://doi.org/10.1007/s11856-018-1770-5
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DOI: https://doi.org/10.1007/s11856-018-1770-5