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Two weak consequences of 0#

Published online by Cambridge University Press:  12 March 2014

M. Gitik ,
M. Magidor  and
H. Woodin
M. Gitik
Affiliation:
Department of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
M. Magidor
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel
H. Woodin
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, California 91125
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Abstract

It is proven that the following statement:

“there exists a club C ⊆ κ such that every α ∈ C is an inaccessible cardinal in L and, for every δ a limit point of C, C ∩ δ is almost contained in every club of δ of L”

is equiconsistent with a weakly compact cardinal if δ = ℵ1, and with a weakly compact cardinal of order 1 if δ = ℵ2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 50 , Issue 3 , September 1985 , pp. 597 - 603
Copyright
Copyright © Association for Symbolic Logic 1985

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References

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