Sequential convergences in $\ell$-groups without Urysohn’s axiom

Sequential Convergences on Generalized Boolean Algebras

In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.

The reinforcement axiom under sequential positional rules

The reinforcement axiom roughly states that when an alternative is selected by two di§erent constituencies, it must also be selected by their union. Hare and Coombs rules are special cases of sequential positional voting rules which are known to violate this axiom. In this paper, we Örst show that reinforcement can be violated by all such rules. We then evaluate, by the use of Monte Carlo simul...

Stochastic Dominance Analysis Without the Independence Axiom

Two-Stage Lotteries without the Reduction Axiom

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Rowbottom cardinals without the Axiom of Choice

We show that for all natural numbers n, the theory “ZF +DCאn + אω is a Rowbottom cardinal carrying a Rowbottom filter” has the same consistency strength as the theory “ZFC + There exists a measurable cardinal”. In addition, we show that the theory “ZF + אω1 is an ω2-Rowbottom cardinal carrying an ω2-Rowbottom filter and ω1 is regular” has the same consistency strength as the theory “ZFC + There...