Choice and complexity

TL;DR: This dissertation aims to clarify the role of language in the development of Complexity and investigates the role that language plays in the design of models and their application to complex systems.

TL;DR: Different formulations and measures that may be used for evaluating the complexity of systems are gathered in this Technical Note and might be useful for describing aspects of military complex systems.

TL;DR: In this paper, a general definition of an aggregation procedure is proposed and a hierarchy of results (possible/impossible, computable/non computable, easy/hard) is illustrated by several examples.

TL;DR: In this article, a review of multiperson decision making from the perspective of social choice theory and the theory of elections is presented, interweaving abstract theory and practical concerns that deserve consideration in evaluating alternative election methods and designing good election systems.

TL;DR: The postulate of economic rationality (or "maximizing" behavior) is the cornerstone of present-day microeconomic theory as discussed by the authors, and it is popular to model consumers or business firms as farsighted maximizers of lifetime utility or profits.

Abstract: In the beginning the author sketches a proof of the equivalence of the set theory of Bernays I I I 49, where two membership relations e and r\ are used, to that of Godel VI 112 and Mostowski IV 129, where only e is used. The author proves, in a slightly different but hardly more illuminating way, the results of Rosser-Wang XVI 145, Novak XVI 273, and Mostowski XVI 274, which establish the essential equivalence of the Zermelo-Fraenkel set theory to the von Neumann-Bernays set theory. Later the author defines, within the framework of the von Neumann-Bernays set theory, the notion of a class being nameable, or definable, relative to sets. He mentions that it is consistent to assume that all classes are nameable relative to sets, and from this, by a simple diagonal argument, he shows that there is a sentence of the form 3BVy(y « B <-• 3A(6(A, y))), where 0(A, y) contains no class variables other than the free variable A, which is not a theorem of the von Neumann-Bernays set theory (this is a new proof of a result somewhat weaker than that of Mostowski XVI 274). Each class nameable relative to sets can be given a name which is a set. The relation 'x is a member of the class whose name is y' is expressible by a formula of the form 3A6(A, x, y), where 0(A, x, y) contains no class variable other than the free variable A, but is shown by the author not to be expressible by a formula without class variables. The author also mentions some consequences of the result of Myhill XX 80 that the hypothesis that all classes are nameable is consistent with the von Neumann-Bernays set theory. I t is known that the proof of Myhill XX 80 establishes his result only upon the assumption that the von Neumann-Bernays set theory stays consistent when it is augmented by Godel's axiom of constructibility, V = L, and by the axiom schema of induction 6(0) A Vn(6(n) ->• 6(n 41)) -»Vn0(n), where 6 is any formula (which may contain also bound class variables). AZRIEL LEVY