Ultrafilter lemma
Ultrafilter lemma In mathematics, the ultrafilter lemma states that every filter is a subset of some ultrafilter, i.e. some maximal proper filter. ...
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Talk:Ultrafilter lemma
Talk:Ultrafilter lemma Is "X A" supposed to be "X ... why is this article not situated at Ultrafilter Lemma, meaning why is "lemma" capital? Thanks! Oleg Alexandrov 05:37, ...
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Ultrafilter
Ultrafilter In the mathematical field of set theory, an ultrafilter on a set X is a collection ... filter; the new defining characteristic of an ultrafilter is that every subset of X is ... X\A is an element of the ultrafilter (here X\A is the relative complement ... Formal definition Given a set X, an ultrafilter on X is a set U ...
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List of lemmas
... of conjectures. Summation by parts Abel's lemma Artin-Rees lemma (commutative algebra) Borel's lemma (partial differential equations) Borel-Cantelli lemma (probability theory) Burnside's lemma Covering lemma Dehn's lemma (geometric ...
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Category:Lemmas
Category:Lemmas In mathematics, a lemma is an auxiliary theorem which is typically ... stone to prove a bigger theorem. See lemma for a more detailed explanation. Pages in ... pages in this section of this category. * Lemma (mathematics) List of lemmas B Borel's lemma Borel-Cantelli lemma Burnside's lemma C Closed and ...
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Boolean prime ideal theorem
... filters on sets is known as the ultrafilter lemma. Other theorems are obtained by considering different ... with respect to the dual order. The ultrafilter lemma states that every filter on a set ... contained within some maximal (proper) filter -- an ultrafilter. Recall that filters on sets are ...
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List of mathematics articles (S-U)
... Sampling fraction -- Sampling (statistics) -- Sangaku -- Sard's lemma -- Sarkovskii's theorem -- Satanic square -- Satisfiability -- Sato ... Sims algorithm -- Schreier vector -- Schreier's subgroup lemma -- Schröder-Bernstein Theorem -- Schrödinger equation -- Schrödinger method ... Schur polynomial -- Schur's inequality -- Schur's lemma -- Schur's theorem -- Schwartz-Zippel lemma and testing polynomial identities -- Schwarz–Ahlfors–Pick theorem -- Schwarz-Christoffel mapping -- Schwarz criterion -- Schwarz lemma -- Schwarz reflection principle -- Schwarz triangle -- Schwarzian ...
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Hyperreal number
... given a set-theoretic object called an ultrafilter, but the ultrafilter itself cannot be explicitly constructed. (Kanovei and ... that matter is given by any free ultrafilter U on the natural numbers; these can ... U, directly in terms of the free ultrafilter U; the two are equivalent. The field ... if we had chosen a different free ultrafilter V, the quotient field A/U ...
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List of mathematical proofs
... π theorem (proof in progress) Burnside's lemma Cantor's theorem Cantor–Bernstein–Schroeder theorem Cayley's ... Euler's theorem Five color theorem Five lemma Fundamental theorem of arithmetic Gauss-Markov theorem ... Borel theorem Intermediate value theorem Itô's lemma König's lemma König's theorem (to do) Lagrange's ... Rice's theorem Rolle's theorem Splitting lemma squeeze theorem Sum rule in differentiation ...
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Talk:Boolean prime ideal theorem
Talk:Boolean prime ideal theorem ultrafilter lemma "Apparently, the ultrafilter lemma also implies BPI, such that both statements ... rather convoluted proof of this, showing that ultrafilter lemma-->compactness theorem-->BPI for free ...
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