Weak covering and the tree property

The strong tree property and weak square

We show that it is consistent, relative to ω many supercompact cardinals, that the super tree property holds at אn for all 2 ≤ n < ω but there are weak square and a very good scale at אω .

Schur-Pair Property and the Structure of Varietal Covering Groups

The Jensen Covering Property

The Jensen covering lemma says that either L has a club class of indiscernibles, or else, for every uncountable set A of ordinals, there is a set B ∈ L with A ⊆ B and card(B) = card(A). One might hope to extend Jensen’s covering lemma to richer weasels, that is, to inner models of the form L[ ~ E] where ~ E is a coherent sequence of extenders of the kind studied in Mitchell-Steel [MiSt]. The pa...

Weak Banach-Saks property in the space of compact operators

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

Covering Property Axiom CPA

Draft of March 11, 2001. We still plan to make considerable changes to this manuscript. Comments and list of typos are welcome!