Hamkins and Löwe asked whether there can be a model N of set theory with the property that N ≡ N [H] whenever H is a generic collapse of a cardinal of N onto ω. We obtain a lower bound, a cardinal κ with a κrepeat point, for the consistency of such a model. We do not know how to construct such a model, under any assumption. We do construct, from a cardinal κ with o(κ) = κ, a model N which satis...

We combine methods from convex analysis, based on a function of Simon Fitzpatrick, with a fine recent idea due to Voisei, to prove maximality of the sum of two maximal monotone operators in Banach space under various natural transversality conditions.

We study the implementation of social choice rules in environments with externalities. prove impossibility implementing efficient and α-individually rational dominant strategies. that α-core is implementable Nash equilibrium under mild restrictions discuss maximality minimality our results. extend analysis to weakly rules.

In this paper, we study the maximal pattern discovery problem in a given sequence for the class ERP of flexible patterns with applications to text mining, where a flexible pattern is a sequence of constant and wildcards for possibly empty strings such as AB*B*ABC, and also known as erasing regular patterns. We first discuss the framework of optimal pattern discovery for predictive mining and te...

This article presents an axiomatic analysis of the best choice decision problem from a reflexive crisp binary relation on a finite set (a digraph). With respect to a transitive digraph, optimality and maximality are usually accepted as the best fitted choice axioms to the intuitive notion of best choice. However, beyond transitivity (resp. acyclicity), optimality and maximality can characterise...

This paper is about the alethic aspect of epistemic rationality. The most common approaches to this are either normative (what a reasoner ought to/may believe?) or evaluative (how rational reasoner?), where usually comparative (one assessed compared another). These often present problems with blindspots. For example, believe currently true blindspot? Is she permitted to? Consequently, these fai...