Assuming the existence of a weakly compact hypermeasurable cardinal we prove that in some forcing extension ℵω is a strong limit cardinal and ℵω+2 has the tree property. This improves a result of Matthew Foreman (see ).
Sy-David Friedman. Ajdin Halilović. "The tree property at ℵω+2." J. Symbolic Logic 76 (2) 477 - 490, June 2011. https://doi.org/10.2178/jsl/1305810760