Public choicePublic choice, or public choice theory, is "the use of economic tools to deal with traditional problems of political science". Its content includes the study of political behavior. In political science, it is the subset of positive political theory that studies self-interested agents (voters, politicians, bureaucrats) and their interactions, which can be represented in a number of ways – using (for example) standard constrained utility maximization, game theory, or decision theory.
Group (mathematics)In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).
Axiom of choiceIn mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by arbitrarily choosing one element from each set, even if the collection is infinite. Formally, it states that for every indexed family of nonempty sets, there exists an indexed set such that for every .
Axiom of dependent choiceIn mathematics, the axiom of dependent choice, denoted by , is a weak form of the axiom of choice () that is still sufficient to develop most of real analysis. It was introduced by Paul Bernays in a 1942 article that explores which set-theoretic axioms are needed to develop analysis. A homogeneous relation on is called a total relation if for every there exists some such that is true. The axiom of dependent choice can be stated as follows: For every nonempty set and every total relation on there exists a sequence in such that for all In fact, x0 may be taken to be any desired element of X.
