set of axioms
51Upper set — The powerset algebra of the set {1,2,3,4} with the upset colored green. In mathematics, an upper set (also called an upward closed set or just an upset) of a partially ordered set (X,≤) is a subset U with the property that x is in …
52Axiom of power set — In mathematics, the axiom of power set is one of the Zermelo Fraenkel axioms of axiomatic set theory.In the formal language of the Zermelo Fraenkel axioms, the axiom reads::forall A , exists P , forall B , [B in P iff forall C , (C in B… …
53Simplicial set — In mathematics, a simplicial set is a construction in categorical homotopy theory which is a purely algebraic model of the notion of a well behaved topological space. Historically, this model arose from earlier work in combinatorial topology and… …
54Derived set (mathematics) — In mathematics, more specifically in point set topology, the derived set of a subset S of a topological space is the set of all limit points of S. It is usually denoted by S′. The concept was first introduced by Georg Cantor in 1872 and he… …
55Positive set theory — In mathematical logic, positive set theory is the name for a class of alternative set theories in which the axiom of comprehension* {x mid phi} exists holds for at least the positive formulas phi (the smallest class of formulas containing atomic… …
56Alternative set theory — Generically, an alternative set theory is an alternative mathematical approach to the concept of set. It is a proposed alternative to the standard set theory. Some of the alternative set theories are: *the theory of semisets; *rough set theory;… …
57Cylinder set — In mathematics, a cylinder set is the natural open set of a product topology. Cylinder sets are particularly useful in providing the base of the natural topology of the product of a countable number of copies of a set. If V is a finite set, then… …
58Ordinal definable set — In mathematical set theory, a set S is said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first order formula. Ordinal definable sets were introduced by Gödel (1965). A drawback to this… …
59Inductive set (axiom of infinity) — In the context of the axiom of infinity, an inductive set (also known as a successor set) is a set X with the property that, for every x in X, the successor x of x is also an element of X. An example of an inductive set is the set of natural… …
60Internal Set Theory — Die Internal Set Theory (keine übliche deutsche Übersetzung bekannt) ist eine rein syntaktische Version der Nichtstandard Analysis, die 1977 von Edward Nelson eingeführt wurde. Anders als im modelltheoretischen Ansatz werden Infinitesimale nicht… …
