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A Gitik iteration with nearly Easton factoring

Published online by Cambridge University Press:  12 March 2014

William J. Mitchell
William J. Mitchell*
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611, USA, E-mail: mitchell@math.ufl.edu
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Abstract

We 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 2 , June 2003 , pp. 481 - 502
Copyright
Copyright © Association for Symbolic Logic 2003

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References

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