534 articles
Uniformization (set theory)
Uniformization in set theory is the operation of choosing one point from each nonempty section of a relation, posed as a problem by Luzin in 1930.
Union (set theory)
The union, or set union, of two sets is the set of all objects belonging to at least one of them, written A ∪ B.
Univalence axiom
The univalence axiom, introduced by Vladimir Voevodsky, states that identity of types is equivalent to equivalence of types, forming the basis of homotopy type theory.
Universal quantification
Universal quantification, marked by the universal quantifier ∀, is the logical operation asserting a formula holds of every object in a domain, one of the two standard quantifiers of predicate logic.
Universal Turing machine
A universal Turing machine is a Turing machine that can simulate any other Turing machine given its encoding and input, described by Alan Turing in 1936.
Vacuous truth
Vacuous truth, or a vacuously true statement, is a statement true only because its subject class is empty, like a conditional with a false antecedent in classical logic.
Variational autoencoder
A variational autoencoder, or VAE, is a deep generative model introduced by Diederik P. Kingma and Max Welling in their December 2013 paper "Auto-Encoding Variational Bayes."
Venn diagram
A Venn diagram, also called a set diagram, represents sets as overlapping closed curves that divide the plane into all 2^n possible intersections; John Venn named and defined it in 1880.
Vertical bar
The vertical bar, also called the pipe, is a glyph, encoded as U+007C, that serves as a punctuation mark, a mathematical symbol, and a heavily used character in computing.
Video tracking
Video tracking is the computer vision task of following one or more moving objects across a sequence of video frames, given an initial location such as a bounding box.
Von Neumann universe
The von Neumann universe, or cumulative hierarchy, is the class V of all well-founded sets, built from the empty set in transfinite stages indexed by the ordinals.
Von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory (NBG) is a finitely axiomatizable axiomatic set theory whose objects are classes; it proves exactly the same statements about sets as ZFC.
Wacław Sierpiński
Wacław Sierpiński, fully Wacław Franciszek Sierpiński, was a Polish mathematician (1882–1969) who worked in set theory and number theory, founded the journal Fundamenta Mathematicae, and gave his name to the Sierpiński triangle and carpet.
Wason selection task
The Wason selection task is a four-card logic puzzle devised by psychologist Peter Wason in 1966, where most people fail to pick the cards that can test the rule.
Well-formed formula
A well-formed formula, abbreviated WFF and pronounced "whiff", is a finite sequence of symbols constructed according to the grammar of a formal language like propositional or first-order logic.
Well-order
A well-order (well-ordering) is a linear order on a set in which every non-empty subset has a least element, exemplified by the usual order on the natural numbers.
Well-ordering theorem
The well-ordering theorem, or well-ordering axiom, states that every set can be given a well ordering. Proved by Ernst Zermelo in 1904, it is equivalent to the axiom of choice over ZF.
Whitehead problem
The Whitehead problem, asked by J.H.C. Whitehead around 1950, asks whether every abelian group with Ext(A, Z) = 0 is free; Shelah proved it independent of ZFC in 1974.
William Lawvere
William Lawvere, also known as F. William Lawvere or F. W. Lawvere, was an American category theorist (1937 to 2023) known for ETCS, Lawvere theories, and elementary topos axioms.
Z notation
The Z notation, also known as the Z specification language, is a formal specification language based on typed set theory and predicate logic, developed at Oxford around 1980.
Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory (ZF) is the standard axiom system for set theory, the foundation for modern mathematics; with the axiom of choice it is ZFC.
Zero–one law (first-order logic)
The zero–one law in first-order logic says any fixed first-order sentence holds on a random graph with probability tending to 0 or 1, proved in 1969 and 1976.
Zorn's lemma
Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a set-theoretic principle equivalent to the axiom of choice, used to prove that every vector space has a basis.
μ-calculus
The μ-calculus, also called the modal μ-calculus, is a temporal logic extending modal logic with least and greatest fixpoint operators, defined by Dexter Kozen in 1983.