We give an affirmative answer to Brendle’s and Hrušák’s question of whether the club principle together with h > א1 is consistent. We work with a class of axiom A forcings with countable conditions such that q ≥n p is determined by finitely many elements in the conditions p and q and that all strengthenings of a condition are subsets, and replace many names by actual sets. There are two types o...

Proof. Without loss of generality, we only need to prove for the case s= 1, as ρ satisfies Axioms A1-A5 if and only if 1 s ρ satisfies Axioms A1-A5 (with s= 1 in Axiom A3). The “only if” part. First, we show that (2) holds for any X ∈L∞(Ω,F , P ). Define the set function ν(E) := ρ(1E),E ∈F . Then, it follows from Axiom A2 and A3 that ν is monotonic, ν(∅) = 0, and ν(Ω) = 1. ForM ≥ 1, define LM :...

We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

This research is designed to study consumers’ purchasing attitudes to counterfeit luxury goods on electronic marketplaces (e-marketplaces). And two research hypotheses are proposed in this research. Based on data analysis of 243 samples, this study explores the dimensions of consumer attitudes (morality and law, accessibility, burden-bearing, function effectiveness, economical efficiency) and m...

If the Wholeness Axiom WA0 is itself consistent, then it is consistent with v=hod. A consequence of the proof is that the various Wholeness Axioms are not all equivalent. Additionally, the theory zfc+wa0 is finitely axiomatizable. The Wholeness Axioms, proposed by Paul Corazza, occupy a high place in the upper stratosphere of the large cardinal hierarchy. They are intended as weakenings of the ...