A Gitik iteration with nearly Easton factoring
Keyword(s):
AbstractWe reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every ν ∈ C is inaccessible in the ground model.Unlike the forcing used by Gitik, the iterated forcing ℛλ+1 used in this paper has the property that if λ is a cardinal less then κ then ℛλ+1 can be factored in V as ℛκ+1 = ℛλ+1 × ℛλ+1,κ where ∣ℛλ+1∣ ≤ λ+ and ℛλ+1,κ does not add any new subsets of λ.
Keyword(s):
Keyword(s):
1976 ◽
Vol 41
(2)
◽
pp. 481-482
◽
2012 ◽
Vol 77
(3)
◽
pp. 1011-1046
◽
Keyword(s):
Keyword(s):
Keyword(s):