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 prope...
We show that many singular cardinals above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle fin ,D introduced in [3]. For such ult...
In this paper, we investigate the extent to which techniques used in [10], [2], and [3] -- developed to prove coloring theorems at successors of singular cardinals of uncountable c...
The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form ...