group theory, the correspondence theorem (also the lattice theorem, and variously and ambiguously the third and fourth isomorphism theorem) states that if...

isomorphism theorem. The first four statements are often subsumed under Theorem D below, and referred to as the lattice theorem, correspondence theorem, or fourth...

kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every Sahlqvist formula is canonical, and corresponds...

most basic form, the theorem asserts that given a field extension E/F that is finite and Galois, there is a one-to-one correspondence between its intermediate...

it follows as a consequence of Lafforgue's theorem. In mathematics, the classical Langlands correspondence is a collection of results and conjectures...

correspondence. Seen at a more abstract level, the correspondence can be restated as shown in the following table. Especially, the deduction theorem specific...

Kähler manifold. The theorem can be considered a vast generalisation of the Narasimhan–Seshadri theorem which defines a correspondence between stable vector...

seven Principles cited in the esoteric book The Kybalion. Correspondence theorem, theorem regarding the relation between subgroups and groups in group...

In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability...

logic) Richardson's theorem (mathematical logic) Robinson's joint consistency theorem (mathematical logic) Sahlqvist correspondence theorem (modal logic) Soundness...

geometry, and gauge theory, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold...

every 1 ≤ m ≤ k. This follows by induction, using Cauchy's theorem and the Correspondence Theorem for groups. A proof sketch is as follows: because the center...

In mathematics, the Robinson–Schensted–Knuth correspondence, also referred to as the RSK correspondence or RSK algorithm, is a combinatorial bijection...

Maximum theorem, f ∗ {\displaystyle f^{*}} is continuous. It remains to verify that C ∗ {\displaystyle C^{*}} is an upper hemicontinuous correspondence with...

terms of ordinary characters. All three main theorems are stated in terms of the Brauer correspondence. There are many ways to extend the definition...

In number theory, the Green–Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long...

}{X^{j}/j!}} . The correspondence between Lie groups and Lie algebras includes the following three main results. Lie's third theorem: Every finite-dimensional...

Jacobson–Bourbaki theorem implies both the usual Galois correspondence for subfields of a Galois extension, and Jacobson's Galois correspondence for subfields...

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving...

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the...

procedures for mixed monotone mappings. Kakutani fixed-point theorem: Every correspondence that maps a compact convex subset of a locally convex space...

theory, the Takagi existence theorem states that for any number field K there is a one-to-one inclusion reversing correspondence between the finite abelian...

who published a proof of it in 1937. The theorem can be interpreted as providing a one-to-one correspondence between distributive lattices and partial...

Cantor–Bernstein–Schröder theorem. Cantor's 1874 Crelle paper was the first to invoke the notion of a 1-to-1 correspondence, though he did not use that...

establishes a bijective correspondence between affine algebraic varieties and prime ideals of polynomial rings. Hilbert's syzygy theorem concerns the relations...

mathematical support to the correspondence principle. The reason is that Ehrenfest's theorem is closely related to Liouville's theorem of Hamiltonian mechanics...

Nonabelian Hodge correspondence Kobayashi–Hitchin correspondence Stable vector bundle Donaldson, S. K. (1983), "A new proof of a theorem of Narasimhan and...

In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system...