set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory. Alternative set theories include: Vopěnka's alternative set theory...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

characteristic of ZFC and related axiomatic set theories such as Von Neumann–Bernays–Gödel set theory (often called NBG) and Morse–Kelley set theory. The cumulative...

a list of articles related to set theory. Algebra of sets Axiom of choice Axiom of countable choice Axiom of dependent choice Zorn's lemma Axiom of power...

of all sets. In its use of classes, AST differs from other alternative set theories such as Morse–Kelley set theory and Von Neumann–Bernays–Gödel set...

Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper...

December 2007. There have been abundant illustrations of pseudoscientific theories-monocausal theories of human behavior that were hailed as "scientific"-that...

as a result of drowning or hypothermia. Since then, many conspiracy theories have been suggested regarding the disaster. These theories have been refuted...

logical positivists thought of scientific theories as deductive theories—that a theory's content is based on some formal system of logic and on basic axioms...

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

formalization of the mathematics of sets; for a listing of different alternative set theories in this sense, see alternative set theory. Set theory may also...

combinations of sets Naive set theory – Informal set theories Symmetric difference – Elements in exactly one of two sets Union (set theory) – Set of elements...

Alternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition with Einstein's theory...

axiom of choice, exploring alternative set theories where the axiom does not hold. choice set A set constructed from a collection of non-empty sets by selecting...

some constructive theories are indeed motivated by their interpretability in type theories. In addition to rejecting the principle of excluded middle (...

In set theory, the intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B , {\displaystyle A\cap B,} is the set containing...

universal set does not exist. However, some non-standard variants of set theory include a universal set. Many set theories do not allow for the existence of a...

systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations...

the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that...

individual when socioeconomic status and environment change). One alternative to set point theory is settling points. With settling points, an increase (or decrease)...

This is a list of notable conspiracy theories. Many conspiracy theories relate to supposed clandestine government plans and elaborate murder plots. They...

algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic...

Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness...

of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set...

contradictions within modern axiomatic set theory. Set theory as conceived by Georg Cantor assumes the existence of infinite sets. As this assumption cannot be...

set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory (ZF)...

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. Writing A = { 1 , 2 , 3 , 4 } {\displaystyle...

scientific theories are discarded in their entirety, such as the replacement of the phlogiston theory by energy and thermodynamics. Some theories known to...

appear in order theory, model theory, and set theory, but can also be found in topology, from which they originate. The dual notion of a filter is an ideal...