Assuming the existence of a λ⁺-hypermeasurable cardinal κ, where λ is the first weakly compact cardinal above κ, we prove that, in some forcing extension, κ is still measurable, κ⁺⁺ has the tree property and . If the assumption is strengthened to the existence of a θ -hypermeasurable cardinal (for an arbitrary cardinal θ > λ of cofinality greater than κ) then the proof can be generalized to get .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-4,
author = {Sy-David Friedman and Ajdin Halilovi\'c},
title = {The tree property at the double successor of a measurable cardinal $\kappa$ with $2^{$\kappa$}$ large},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {55-64},
zbl = {1326.03060},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-4}
}
Sy-David Friedman; Ajdin Halilović. The tree property at the double successor of a measurable cardinal κ with $2^{κ}$ large. Fundamenta Mathematicae, Tome 220 (2013) pp. 55-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm223-1-4/