nonprincipal ultrafilter

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• Ultrafilter — In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). An ultrafilter may be considered as a finitely additive measure. Then every subset of X is …   Wikipedia

• Nakamura number — In cooperative game theory and social choice theory, the Nakamura number measures the degree of rationality of preference aggregation rules (collective decision rules), such as voting rules. It is an indicator of the extent to which an… …   Wikipedia

• Property of Baire — A subset A of a topological space X has the property of Baire (Baire property) if it differs from an open set by a meager set; that is, if there is an open: Usubseteq Xsuch that: ADelta Uis meager (here, Delta; denotes the symmetric… …   Wikipedia

• Piecewise syndetic set — In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. Let mathcal{P} f(mathbb{N}) denote the set of finite subsets of mathbb{N}. Then a set S sub mathbb{N} is called piecewise syndetic if there exists G …   Wikipedia

• New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for …   Wikipedia

• Filter (mathematics) — The powerset algebra of the set {1,2,3,4} with the upset colored green. The green elements make a principal ultrafilter on the lattice. In mathematics, a filter is a special subset of a partially ordered set. A frequently used special case is the …   Wikipedia