This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive...

have set-like collections while differing from sets so as to avoid paradoxes, especially Russell's paradox (see § Paradoxes). The precise definition of "class"...

set theory is inconsistent. Prior to Russell's paradox (and to other similar paradoxes discovered around the time, such as the Burali-Forti paradox)...

After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems...

presented his paradox, not necessarily a theory Cantor—who, as mentioned, was aware of several paradoxes—presumably had in mind. Axiomatic set theory was developed...

in the development of modern logic and set theory. Thought-experiments can also yield interesting paradoxes. The grandfather paradox, for example, would...

formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice...

condition, leading to paradoxes such as Russell's paradox in naïve set theory. naive set theory 1.  Naive set theory can mean set theory developed non-rigorously...

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...

contradict themselves Banach–Tarski paradox – Geometric theorem Galileo's paradox – Paradox in set theory Paradoxes of set theory Pigeonhole principle – If there...

In set theory, the complement of a set A, often denoted by A ∁ {\displaystyle A^{\complement }} (or A′), is the set of elements not in A. When all elements...

"Set Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University Suppes, Patrick (1972) [1960], Axiomatic Set Theory,...

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

Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is...

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...

included as one of its members). This paradox prevents the existence of a universal set in set theories that include either Zermelo's axiom of restricted comprehension...

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...

This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list...

set theory (KP), pronounced /ˈkrɪpki ˈplɑːtɛk/, is an axiomatic set theory developed by Saul Kripke and Richard Platek. The theory can be thought of as...

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...

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be...

axiom of unrestricted comprehension is not supported by modern set theory, and Curry's paradox is thus avoided. Girard's paradox List of paradoxes Richard's...

Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an uncountable set. The paradox arises from...

In set theory, Cantor's paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal...

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 set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction...

In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary...

number paradox – On the smallest non-interesting number Paradoxes of set theory Richard's paradox – Apparent contradiction in metamathematics Griffin 2003...

philosophy of mathematics NP (complexity) – Complexity class used to classify decision problems Paradoxes of set theory Transcomputational problem – Class of computational...

to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory. The...