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Backwards easton forcing and 0#

Published online by Cambridge University Press:  12 March 2014

M. C. Stanley
M. C. Stanley*
Affiliation:
Department of Mathematics and Computer Science, San Jose State University, San Jose, California 95192
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Abstract

It is shown that if κ is an uncountable successor cardinal in L[0#], then there is a normal tree T ϵ L[0#] of height κ such that 0# ∉ L[T], yet T is < κ-distributive in L[0#]. A proper class version of this theorem yields an analogous L[0#]-definable tree such that distinct branches in the presence of 0# collapse the universe. A heretofore unutilized method for constructing in L[0#] generic objects for certain L-definable forcings and “exotic sequences”, combinatorial principles introduced by C. Gray, are used in constructing these trees.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 53 , Issue 3 , September 1988 , pp. 809 - 833
Copyright
Copyright © Association for Symbolic Logic 1988

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References

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