In set theory, Kőnig's theorem states that if the axiom of choice holds, I is a set, κ i {\displaystyle \kappa _{i}} and λ i {\displaystyle \lambda _{i}}...

In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem...

Kőnig. Kőnig's theorem (graph theory), named after his son Dénes Kőnig. König's theorem (kinetics), named after the German mathematician Samuel König...

certainly wrong. Therefore Kőnig's assumption must be in error. Am I wrong or am I right? Cantor was wrong. Today Kőnig's assumption is generally accepted...

McCoart, Theory of finite and infinite graphs, Birkhäuser, 1990, ISBN 0-8176-3389-8. Kőnig's theorem (graph theory) Kőnig's theorem (set theory) is due...

provability in first-order logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language)...

Kőnig's theorem (set theory) Kőnig's theorem (graph theory) Lagrange's theorem (group theory) Lagrange's theorem (number theory) Liouville's theorem (complex...

Kőnig's lemma or Kőnig's infinity lemma is a theorem in graph theory due to the Hungarian mathematician Dénes Kőnig who published it in 1927. It gives...

n ) {\displaystyle P(n)} are true as a consequence of Kruskal's theorem and Kőnig's lemma. For each n, Peano arithmetic can prove that P ( n ) {\displaystyle...

In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there...

mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an antichain...

as König's theorem, while Roberts & Tesman (2009) refer to this version as the Kőnig-Egerváry theorem. The bipartite graph version is called Kőnig's theorem...

In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which...

Kőnig's theorem (bipartite graphs) Kövari–Sós–Turán theorem (graph theory) Kruskal–Katona theorem (combinatorics) Kuratowski's theorem (graph theory)...

first-order theory of some version of set theory. The Löwenheim–Skolem theorem dealt a first blow to this hope, as it implies that a first-order theory which...

equations. Noether's second theorem is sometimes used in gauge theory. Gauge theories are the basic elements of all modern field theories of physics, such as...

foreshadowed by results in set theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse...

mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of...

in a maximum independent set equals the number of edges in a minimum edge covering; this is Kőnig's theorem. An independent set that is not a proper subset...

Brouwer's theorem can be proved in the system WKL0, and conversely over the base system RCA0 Brouwer's theorem for a square implies the weak Kőnig's lemma...

mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict...

Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published...

about infinite sets and their cardinalities, related to König's theorem on the sums and products of cardinals. KP Kripke–Platek set theory Kripke 1.  Saul...

Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language...

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

bipartite graphs, are both equivalent to Kőnig's theorem relating the sizes of maximum matchings, maximum independent sets, and minimum vertex covers in bipartite...

classical Kőnig's lemma, whereas the converse implication does not hold, since Kőnig's lemma is equivalent to countable choice from finite sets in this...

{\mathfrak {c}}=2^{\aleph _{0}}} can be any cardinal consistent with Kőnig's theorem. A result of Solovay, proved shortly after Cohen's result on the independence...

economize on the number of switches while achieving a maximum matching. Kőnig's theorem states that, in bipartite graphs, the maximum matching is equal in...

In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that,...