Shelah's strong covering property and CH in V [r ]

A COVERING PROPERTY IN PRINCIPAL BUNDLES

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

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!

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...

Schur-Pair Property and the Structure of Varietal Covering Groups

Strong covering without squares

The study of “covering lemmas” started with Jensen [DeJe] who proved in 1974–5 that in the absence of 0 there is a certain degree of resemblance between V and L. More precisely, if 0 does not exist then for every set of ordinals X there exists a set of ordinals Y ∈ L such that X ⊆ Y and V 2 |Y | = max{|X|,א1}. There is no hope of covering countable sets by countable ones in general, because doi...