How many normal measures can ${\aleph }_{\omega +1}$ carry?

Arthur W. Apter. "How many normal measures can $ℵ_{ω+1}$ carry?." Fundamenta Mathematicae 191.1 (2006): 57-66. <http://eudml.org/doc/282648>.

@article{ArthurW2006,
abstract = {We show that assuming the consistency of a supercompact cardinal with a measurable cardinal above it, it is possible for $ℵ_\{ω+1\}$ to be measurable and to carry exactly τ normal measures, where $τ ≥ ℵ_\{ω+2\}$ is any regular cardinal. This contrasts with the fact that assuming AD + DC, $\{ℵ_\{ω+1\}\}$ is measurable and carries exactly three normal measures. Our proof uses the methods of [6], along with a folklore technique and a new method due to James Cummings.},
author = {Arthur W. Apter},
journal = {Fundamenta Mathematicae},
keywords = {supercompact cardinal; measurable cardinal; normal measure; indestructibility; gap forcing; symmetric inner model},
language = {eng},
number = {1},
pages = {57-66},
title = {How many normal measures can $ℵ_\{ω+1\}$ carry?},
url = {http://eudml.org/doc/282648},
volume = {191},
year = {2006},
}

TY - JOUR
AU - Arthur W. Apter
TI - How many normal measures can $ℵ_{ω+1}$ carry?
JO - Fundamenta Mathematicae
PY - 2006
VL - 191
IS - 1
SP - 57
EP - 66
AB - We show that assuming the consistency of a supercompact cardinal with a measurable cardinal above it, it is possible for $ℵ_{ω+1}$ to be measurable and to carry exactly τ normal measures, where $τ ≥ ℵ_{ω+2}$ is any regular cardinal. This contrasts with the fact that assuming AD + DC, ${ℵ_{ω+1}}$ is measurable and carries exactly three normal measures. Our proof uses the methods of [6], along with a folklore technique and a new method due to James Cummings.
LA - eng
KW - supercompact cardinal; measurable cardinal; normal measure; indestructibility; gap forcing; symmetric inner model
UR - http://eudml.org/doc/282648
ER -