Singular cohomology in \(L\) (Q1238810)

\textit{D. M. Kan} and \textit{G. M. Whitehead} [Proc. Am. Math. Soc. 12, 24-25 (1961; Zbl 0109.15801)] mention that the following proposition in algebraic topology is unclear: There does not exist a topological space \(X\) and integer \(n\geq 2\) such that \(H^n(X,\mathbb Z)\cong\mathbb Q(H^n(X,\mathbb Z)\) denotes ordinary singular cohomology with integral coefficients). Assuming \(V=L\) the authors show that the proposition becomes true. The authors use ideas from \textit{S. Shelah}'s recent work on Whitehead's problem [Isr. J. Math. 21, 319-349 (1975; Zbl 0369.02034)]. It is the hope of the authors that this paper will further stimulate interest in the interplay between homological algebra and set theory.