In multiwinner approval voting, the goal is to select k-member committees based on voters' ballots. A well-studied concept of proportionality in this context justified representation (JR) axiom, which demands that no large cohesive group voters remains unrepresented. However, JR axiom may conflict with other desiderata, such as coverage (maximizing number who approve at least one committee memb...

‎let ${x_{alpha}:alphainlambda}$ be a collection of topological spaces‎, ‎and $mathcal {g}_{alpha}$ be a grill on $x_{alpha}$ for each $alphainlambda$‎. ‎we consider tychonoffrq{}s type theorem for $x=prod_{alphainlambda}x_{alpha}$ via the above grills and a natural grill on $x$ ‎related to these grills, and present a simple proof to this theorem‎. ‎this immediately yields the classical theorem...

Two-person bargaining problem is considered as to allocate a number of goods between two players. This paper suggests that any non-trivial division of goods cause a non-zero change on the solution of bargaining. So, a axiom of sharing division is presented, as an alternative axiom to Nash’s axiom of independence of irrelevant alternatives and Kalai-Smorodinsky’s axiom of monotonicity. This solu...

We prove criteria for axiom (b1) of [Cluckers, Loeser, b-minimality, http://www.dma.ens.fr/∼cluckers/]. We establish criteria for b-minimality when the auxiliary sorts are small. These criteria show that in many naturally occurring situations, for example in the situation of local fields, axiom (b1) is the only important axiom of b-minimality, in the sense that the other axioms of b-minimality ...

In this note, we give a survey on recent developments pertaining to forcing axioms with emphasis on their characterizations and consequences connected to the Continuum Problem. Nonspecialists in set theory and/or students in mathematics are supposed to be the readers, and thus we tried to make this as self-contained as possible. Due to the limitation on the extent of the article, however, many ...

We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (!2; !2)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen’s combinatorial principles for L at the level !2, and therefore with the existence of an !2-Suslin tree. We also show that the axiom we ...

We introduce a new simple first-order framework for theories whose objects are wellorderings (lists). A system ALT (axiomatic list theory) is presented and shown to be equiconsistent with ZFC (Zermelo Fraenkel Set Theory with the Axiom of Choice). The theory sheds new light on the power set axiom and on Gödel’s axiom of constructibility. In list theory there are strong arguments favoring Gödel’...

The language for the formulation of the interesting statements is, of course, most important. We use first order predicate logic. Our main achievement in this paper is an axiom system which we believe to be more powerful than any other natural general purpose discovery axiom system. We prove soundness of this axiom system in this paper. Additionally we prove that if we remove some of the requir...

If T is a complete theory stronger than ZFFin such that axiom of extensionality for classes + T + (9X) i is consistent for 1 i k (each alone), where i are normal formulae then we showAST + (9X) 1+ +(9X) k + scheme of choice is consistent. As a consequence we get: there is no proper 1-formula inAST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.g. we show axiom of...

In this article, we provide the epistemicentrenchment characterization of the weak version of Parikh’s relevance-sensitive axiom for belief revision — known as axiom (P) — for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the ...