The tree property at the double successor of a measurable cardinal κ with $2^{\kappa }$ large

Sy-David Friedman, and Ajdin Halilović. "The tree property at the double successor of a measurable cardinal κ with $2^{κ}$ large." Fundamenta Mathematicae 223.1 (2013): 55-64. <http://eudml.org/doc/286631>.

@article{Sy2013,
abstract = {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 $2^\{κ\} = κ⁺⁺⁺$. 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 $2^\{κ\} = θ $.},
author = {Sy-David Friedman, Ajdin Halilović},
journal = {Fundamenta Mathematicae},
keywords = {tree property; large cardinals; forcing},
language = {eng},
number = {1},
pages = {55-64},
title = {The tree property at the double successor of a measurable cardinal κ with $2^\{κ\}$ large},
url = {http://eudml.org/doc/286631},
volume = {223},
year = {2013},
}

TY - JOUR
AU - Sy-David Friedman
AU - Ajdin Halilović
TI - The tree property at the double successor of a measurable cardinal κ with $2^{κ}$ large
JO - Fundamenta Mathematicae
PY - 2013
VL - 223
IS - 1
SP - 55
EP - 64
AB - 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 $2^{κ} = κ⁺⁺⁺$. 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 $2^{κ} = θ $.
LA - eng
KW - tree property; large cardinals; forcing
UR - http://eudml.org/doc/286631
ER -