TY - JOUR
T1 - Scales at אω
AU - Sinapova, Dima
AU - Unger, Spencer
N1 - Publisher Copyright:
© 2015, Hebrew University of Jerusalem.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - We show that it is consistent relative to a supercompact cardinal that $${N_\omega }$$ is a strong limit, $${2^{{N_\omega }}} = {N_{\omega + 2}}$$ and $${\square _{{N_\omega },{N_n}}}$$ fails for all n < ω. This gives a partial answer to an old question of Woodin about the consistency of failure of SCH and failure of weak square.
AB - We show that it is consistent relative to a supercompact cardinal that $${N_\omega }$$ is a strong limit, $${2^{{N_\omega }}} = {N_{\omega + 2}}$$ and $${\square _{{N_\omega },{N_n}}}$$ fails for all n < ω. This gives a partial answer to an old question of Woodin about the consistency of failure of SCH and failure of weak square.
UR - http://www.scopus.com/inward/record.url?scp=84945562085&partnerID=8YFLogxK
U2 - 10.1007/s11856-015-1225-1
DO - 10.1007/s11856-015-1225-1
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AN - SCOPUS:84945562085
SN - 0021-2172
VL - 209
SP - 463
EP - 486
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -