Measurable cardinals and the cofinality of the symmetric group

Sy-David Friedman, and Lyubomyr Zdomskyy. "Measurable cardinals and the cofinality of the symmetric group." Fundamenta Mathematicae 207.2 (2010): 101-122. <http://eudml.org/doc/286122>.

@article{Sy2010,
abstract = {Assuming the existence of a P₂κ-hypermeasurable cardinal, we construct a model of Set Theory with a measurable cardinal κ such that $2^\{κ\} = κ⁺⁺$ and the group Sym(κ) of all permutations of κ cannot be written as the union of a chain of proper subgroups of length < κ⁺⁺. The proof involves iteration of a suitably defined uncountable version of the Miller forcing poset as well as the “tuning fork” argument introduced by the first author and K. Thompson [J. Symbolic Logic 73 (2008)].},
author = {Sy-David Friedman, Lyubomyr Zdomskyy},
journal = {Fundamenta Mathematicae},
keywords = {hypermeasurable cardinal; measurable cardinal; Miller forcing; Sacks forcing; lifting},
language = {eng},
number = {2},
pages = {101-122},
title = {Measurable cardinals and the cofinality of the symmetric group},
url = {http://eudml.org/doc/286122},
volume = {207},
year = {2010},
}

TY - JOUR
AU - Sy-David Friedman
AU - Lyubomyr Zdomskyy
TI - Measurable cardinals and the cofinality of the symmetric group
JO - Fundamenta Mathematicae
PY - 2010
VL - 207
IS - 2
SP - 101
EP - 122
AB - Assuming the existence of a P₂κ-hypermeasurable cardinal, we construct a model of Set Theory with a measurable cardinal κ such that $2^{κ} = κ⁺⁺$ and the group Sym(κ) of all permutations of κ cannot be written as the union of a chain of proper subgroups of length < κ⁺⁺. The proof involves iteration of a suitably defined uncountable version of the Miller forcing poset as well as the “tuning fork” argument introduced by the first author and K. Thompson [J. Symbolic Logic 73 (2008)].
LA - eng
KW - hypermeasurable cardinal; measurable cardinal; Miller forcing; Sacks forcing; lifting
UR - http://eudml.org/doc/286122
ER -