The Hirsch index is a number that synthesizes a researcher’s output. It is the maximum number h such that the researcher has h papers with at least h citations each. Woeginger [Woeginger, G. J. (2008a). An axiomatic characterization of the Hirsch-index. Mathematical Social Sciences, 56(2), 224–232; Woeginger, G. J. (2008b). A symmetry axiom for scientific impact indices. Journal of Informetrics...

We prove that a random choice rule satisfies Luce's Choice Axiom if and only its support is correspondence the Weak of Revealed Preference, thus it consists alternatives are optimal according to some preference, then occurs tie-breaking mechanism among such Renyi's Conditioning Axiom. Our result shows is, in precise formal sense, probabilistic version It supports view his own axiom as “canon ra...

We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both 2(δ) and 2δ fail, then δ is subcompact in a class inner model. If in addition 2(δ) fails, we prove that δ is Π21 subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. A...

Basu and Van (1998) present a fundamental framework of child labor with two important axioms: the luxury axiom and the substitution axiom. A number of empirical studies, however, reveal a “wealth paradox”. The current paper has two aims. First, it develops a model that provides an explanation for “the wealth paradox” in light of the luxury axiom and the substitution axiom. Second, it helps unde...

Fuzzy logic adds to bivalent logic an important capability—a capability to reason precisely with imperfect information. Imperfect information is information which in one or more respects is imprecise, uncertain, incomplete, unreliable, vague or partially true. In fuzzy logic, results of reasoning are expected to be provably valid, or p-valid for short. Extended fuzzy logic adds an equally impor...

The well known results on the inner limitations of classical mathematics (L6wenheim-Skolem Theorems, and G6del's Theorems) and the introduction of a host of new set-like concepts, indicate the presence of something which is beyond the grasp of Cantorian set theory. In different ways each limitation expresses a basic uncertainty in Mathematics. GOdel's Theorems essentially express the following:...

In recent publications Alain Connes [1] and John Barrett [2] proposed to change the KO-dimension of the internal space of the standard model in its noncommutative representation [3] from zero to six. This apparently minor modification allowed to resolve the fermion doubling problem [4], and the introduction of Majorana mass terms for the right-handed neutrino. The price which had to be paid was...

A non-trivial, transitive and reflexive binary relation on the set of lotteries satisfying independence that also satisfies any two of the following three axioms satisfies the third: completeness, Archimedean and mixture continuity (Dubra (2011)). This paper generalizes Dubra’s result in two ways: First, by replacing independence with a weaker betweenness axiom. Second, by replacing independenc...

This paper contributes to a theory of rational choice for decisionmakers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of ‘Complete Ignorance’ which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a ‘Principle of Preference-Basedne...

A recently proposed axiom system for André’s central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed independent. Second, whereas most of the original independence models were infinite, finite independence models are available. Moreover, the independence proof for one of...