Sciweavers

Share
AML
2011

A remark on the tree property in a choiceless context

7 years 10 months ago
A remark on the tree property in a choiceless context
We show that the consistency of the theory “ZF + DC + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” follows from the consistency of a proper class of supercompact cardinals. This extends earlier results due to the author showing that the consistency of the theory “ZF + ¬ACω + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” follows from hypotheses stronger in consistency strength than a supercompact limit of supercompact cardinals. A lower bound in consistency strength is provided by a result of Busche and Schindler, who showed that the consistency of the theory “ZF + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” implies the consistency of ADL(R) . We begin by very briefly mentioning some of our conventions and terminology. As usua...
Arthur W. Apter
Added 24 Aug 2011
Updated 24 Aug 2011
Type Journal
Year 2011
Where AML
Authors Arthur W. Apter
Comments (0)
books