In order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are...

interval does not, and order isomorphisms must preserve the existence of least elements. By Cantor's isomorphism theorem, every unbounded countable dense...

In set theory and order theory, the Cantor–Bernstein theorem states that the cardinality of the second type class, the class of countable order types,...

between A and B Cantor's isomorphism theorem: every two countable dense unbounded linear orders are isomorphic Cantor's intersection theorem: a decreasing...

question marks, boxes, or other symbols. In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\displaystyle...

The theorem is named after Felix Bernstein and Ernst Schröder. It is also known as the Cantor–Bernstein theorem or Cantor–Schröder–Bernstein theorem, after...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

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...

no endpoints; Cantor proved that any such countable linear order is isomorphic to the rational numbers: see Cantor's isomorphism theorem. Every categorical...

axiom of choice). The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma (Kelley 1955:33). The Hausdorff maximal principle...

order preserving functions as morphisms. The correspondence above is an isomorphism of categories between Alex and PreOrd. Furthermore, the functor A : P...

In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under...

In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement...

graph Logic gate Boolean analysis Boolean prime ideal theorem Compactness theorem Consensus theorem De Morgan's laws Duality (order theory) Laws of classical...

Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One...

z) = (x ∨ y) ∧ (x ∨ z) holds Being a Boolean algebra Being an order isomorphism. Since partial orders are antisymmetric, the only ones that are self-dual...

of abstract algebra. He adopted this terminology because, using the isomorphism of the categories of Boolean algebras and of Boolean rings, the two notions...

Results Boolean prime ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle...

Results Boolean prime ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle...

must satisfy the sentence saying the real numbers are uncountable. Cantor's theorem states that some sets are uncountable. This counterintuitive situation...

antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (totally ordered subsets)...

& Tamassia (1995a), Theorem 9, p. 118; Baker, Fishburn & Roberts (1971), theorem 4.1, page 18. Garg & Tamassia (1995a), Theorem 15, p. 125; Bertolazzi...

strictly increasing bijection from the former to the latter. Relevant theorems of this sort are expanded upon below. More examples can be given now: The...

Pointwise order of functions Galois connection Order embedding Order isomorphism Closure operator Functions that preserve suprema/infima Dedekind completion...

logic) Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers) Cantor's theorem (set theory, Cantor's diagonal argument) Church–Rosser theorem (lambda...

List of statements independent of ZFC Continuum hypothesis AD+ Cantor's isomorphism theorem K. Devlin and H. Johnsbråten, The Souslin Problem, Lecture Notes...

Results Boolean prime ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle...

An order isomorphism can be characterized as a surjective order embedding. As a consequence, any order embedding f restricts to an isomorphism between...

order-preserving. Given the standard definition of isomorphisms as invertible morphisms, a lattice isomorphism is just a bijective lattice homomorphism. Similarly...

{\displaystyle (Tu-Tv,u-v)\geq 0\quad \forall u,v\in X.} Kachurovskii's theorem shows that convex functions on Banach spaces have monotonic operators as...