Angeltveit, VigleikLind, John A.2017-04-052193-8407http://hdl.handle.net/1885/114498Fix a prime number p and an integer n≥ 0. We prove that if a p-complete spectrum X satisfying a mild finiteness condition has the same mod p cohomology as BP⟨ n⟩ as a module over the Steenrod algebra, then X is weak homotopy equivalent to the p-completion of BP⟨ n⟩.The first author was supported by an ARC Discovery grant. The second author was partially supported by the DFG through SFB-1085, and thanks the Australian National University for hosting him while this research was conducted.application/pdf© Tbilisi Centre for Mathematical Sciences 2015. http://www.springer.com/gp/open-access/authors-rights/self-archiving-policy/2124..."Authors may self-archive the author’s accepted manuscript of their articles on their own websites. Authors may also deposit this version of the article in any repository, provided it is only made publicly available 12 months after official publication or later." from the publisher site (as at 6/04/17).201510.1007/s40062-015-0120-0