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Longer titles found: Axiom of choice (disambiguation) (view), Group structure and the axiom of choice (view), Axiom of Choice (band) (view), Equivalents of the Axiom of Choice (view)

searching for Axiom of choice 41 found (671 total)

alternate case: axiom of choice

Cardinality of the continuum (2,374 words) [view diff] exact match in snippet view article find links to article

be proven within the widely used Zermelo–Fraenkel set theory with axiom of choice (ZFC). Georg Cantor introduced the concept of cardinality to compare

Kolmogorov Medal (238 words) [view diff] exact match in snippet view article find links to article

1093/comjnl/bxh124, ISSN 0010-4620 Martin-Löf, Per (2005), "100 years of Zermelo's axiom of choice: what was the problem with it?", The Computer Journal, 49 (3): 345–350

Kirszbraun theorem (652 words) [view diff] exact match in snippet view article find links to article

theory; for the fully general case, it appears to need some form of the axiom of choice; the Boolean prime ideal theorem is known to be sufficient. The proof

Henry Fool (band) (707 words) [view diff] case mismatch in snippet view article

rock press. It was tagged as "highly recommended" by New Horizons and Axiom Of Choice described it as "quite a feat (with) plenty to offer..." Planet Mellotron

Area (5,316 words) [view diff] exact match in snippet view article find links to article

measure, though not every subset is measurable if one supposes the axiom of choice. In general, area in higher mathematics is seen as a special case of

Constructive nonstandard analysis (160 words) [view diff] exact match in snippet view article find links to article

which can be formalized in a constructive metatheory without the axiom of choice."[1] Erik Palmgren, Developments in Constructive Nonstandard Analysis

Freiling's axiom of symmetry (1,648 words) [view diff] exact match in snippet view article find links to article

which the (generalised) continuum hypothesis is an extension of the axiom of choice. Freiling's argument is not widely accepted because of the following

Measurable cardinal (1,775 words) [view diff] case mismatch in snippet view article find links to article

would contradict the non-triviality of the measure. Thus, assuming the Axiom of Choice, we can infer that κ is a strong limit cardinal, which completes the

Ramsey's theorem (7,887 words) [view diff] no match in snippet view article find links to article

In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)

Nebula Awards Showcase 2013 (595 words) [view diff] case mismatch in snippet view article find links to article

Honey" [Rhysling Award for Short Poem, 2011] (Amal El-Mohtar) "The Axiom of Choice" [Best Short Story nominee, 2011] (David W. Goldman) "Club Story" [essay]

Leonard Gillman (1,073 words) [view diff] case mismatch in snippet view article find links to article

Leonard (June–July 2002). "Two Classical Surprises Concerning the Axiom of Choice and the Continuum Hypothesis" (PDF). American Mathematical Monthly

List of important publications in mathematics (10,144 words) [view diff] exact match in snippet view article find links to article

breakthrough work proved the independence of the continuum hypothesis and axiom of choice with respect to Zermelo–Fraenkel set theory. In proving this Cohen

Chance (TV series) (692 words) [view diff] case mismatch in snippet view article

Alexandra Cunningham & Kem Nunn October 19, 2016 (2016-10-19) 2 2 "The Axiom of Choice" Lenny Abrahamson Alexandra Cunningham October 19, 2016 (2016-10-19)

Set-theoretic definition of natural numbers (758 words) [view diff] exact match in snippet view article find links to article

notion, Card(), and an axiom of cardinality to ZF set theory (without axiom of choice). Axiom of cardinality: The sets A and B are equinumerous if and only

Epistemological solipsism (324 words) [view diff] exact match in snippet view article find links to article

neither validate nor invalidate it. The continuum hypothesis and the axiom of choice, are examples of possible transcendental decision points. Solipsism

Eric Schechter (488 words) [view diff] case mismatch in snippet view article find links to article

Common Errors in Undergraduate Mathematics [2] A Home Page for the Axiom of Choice [3] Schechter is involved in political activism of the democratic socialist

Finite character (352 words) [view diff] case mismatch in snippet view article find links to article

basis. Hereditarily finite set Jech, Thomas J. (2008) [1973]. The Axiom of Choice. Dover Publications. ISBN 978-0-486-46624-8. Smullyan, Raymond M.;

Pejman Hadadi (132 words) [view diff] case mismatch in snippet view article find links to article

Dastan Ensemble (Traditional Crossroads, 1997) "Beyond Denial" with Axiom of Choice (X Dot 25, 1994) "Scattering Stars Like Dust" with Kayhan Kalhor. (Traditional

Felix Hausdorff (7,450 words) [view diff] exact match in snippet view article find links to article

either the well-ordering theorem or the axiom of choice, and as it turned out, is also equivalent to the axiom of choice. Writing in 1908, Arthur Moritz Schoenflies

Cover (topology) (1,376 words) [view diff] exact match in snippet view article

U_{A}\in {\mathcal {O}}} containing A {\displaystyle A} (requiring the axiom of choice). Then C = { U A ∈ O : A ∈ A } {\displaystyle {\mathcal {C}}=\{U_{A}\in

Partially ordered set (5,397 words) [view diff] exact match in snippet view article find links to article

comparable Zorn's lemma – Mathematical proposition equivalent to the axiom of choice A proof can be found here. which always exists and is unique, since

List of lemmas (522 words) [view diff] exact match in snippet view article find links to article

lemma also known as Tukey's lemma Zorn's lemma; equivalent to the axiom of choice Covering lemma Delta lemma Dynkin lemma Fodor's lemma Fixed-point lemma

Injective object (1,031 words) [view diff] exact match in snippet view article find links to article

an injective object is necessarily a divisible group. Assuming the axiom of choice, the notions are equivalent. In the category of (left) modules and

Fréchet filter (950 words) [view diff] exact match in snippet view article find links to article

established by Tarski in 1930, relying on a theorem equivalent to the axiom of choice and is used in the construction of the hyperreals in nonstandard analysis

John Lane Bell (410 words) [view diff] case mismatch in snippet view article find links to article

Models and Independence Proofs. Oxford University Press 2011. The Axiom of Choice. College Publications, 2009. The Continuous and the Infinitesimal in

Horst Herrlich (314 words) [view diff] case mismatch in snippet view article find links to article

and Concrete Categories. Wiley-Interscience Publ., New York. 1990. Axiom of Choice. Springer Lecture Notes Math. vol. 1876. 2006. ISBN 9783540342687.

Bickram Ghosh (641 words) [view diff] case mismatch in snippet view article find links to article

African Arc Music 2002 Kora So Far- Ravi (J.P. Freeman) Terra Nova 2002 Axiom of Choice- Unfolding Narada 2002 Brain Washed- George Harrison Capitol/EMI 2008

Elliott Mendelson (662 words) [view diff] case mismatch in snippet view article find links to article

87(5): 225–233. Elliott Mendelson (1956) "The Independence of a Weak Axiom of Choice", Journal of Symbolic Logic 21(4): 350–366. Sidney Morgenbesser & Elliott

Hopfian object (842 words) [view diff] exact match in snippet view article find links to article

category. For example, assuming Zermelo–Fraenkel set theory with the axiom of choice and working in the category of sets, the hopfian and cohopfian objects

Delta-convergence (542 words) [view diff] case mismatch in snippet view article find links to article

theorem (in the non-separable case) its proof does not depend on the Axiom of Choice. An asymptotic center of a sequence ( x k ) k ∈ N {\displaystyle (x_{k})_{k\in

Intuitionism (2,779 words) [view diff] case mismatch in snippet view article find links to article

Functions Section 1 Informal Introduction; and p. 146-151 Section 7 the Axiom of Choice. Turing, Alan M. (1939). "Systems of Logic Based on Ordinals". Proceedings

Orthonormal basis (2,582 words) [view diff] exact match in snippet view article find links to article

orthonormal basis. (One can prove this last statement without using the axiom of choice.) For concreteness we discuss orthonormal bases for a real, n {\displaystyle

Lebesgue's number lemma (1,109 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \{x_{n}\}} where x n ∈ A n {\displaystyle x_{n}\in A_{n}} by axiom of choice. By sequential compactness, there exists a subsequence { x n k } ,

Dana Scott (1,327 words) [view diff] case mismatch in snippet view article find links to article

James Halpern (Contributions to the Study of the Independence of the Axiom of Choice) and Edgar Lopez-Escobar (Infinitely Long Formulas with Countable Quantifier

Lévy hierarchy (1,368 words) [view diff] exact match in snippet view article find links to article

cardinal there exists a measurable cardinal κ is an n-huge cardinal The axiom of choice The generalized continuum hypothesis The axiom of constructibility:

Cauchy sequence (3,218 words) [view diff] exact match in snippet view article find links to article

Cauchy sequence; this can be proven without using any form of the axiom of choice. Moduli of Cauchy convergence are used by constructive mathematicians

Actor model theory (1,545 words) [view diff] exact match in snippet view article find links to article

Chains Between Events in the Combined Ordering (without using the axiom of choice.) The law of discreteness rules out Zeno machines and is related to

Extensive-form game (3,763 words) [view diff] exact match in snippet view article find links to article

perspective; see Chapter 5. Downloadable free online. Horst Herrlich (2006). Axiom of choice. Springer. ISBN 978-3-540-30989-5., 6.1, "Disasters in Game Theory"

Damian Wilson (2,225 words) [view diff] case mismatch in snippet view article find links to article

Music Video". YouTube. Archived from the original on 22 December 2021. Retrieved 5 July 2020. Official website Headspace official site Axiom of Choice

John Truss (1,423 words) [view diff] case mismatch in snippet view article find links to article

dissertation titled "Some Results about Cardinal Numbers without the Axiom of Choice" which was supervised by Frank Drake. In 1969, he married Priscilla

Michael Fourman (634 words) [view diff] exact match in snippet view article find links to article

Fourman, Michael P.; Scedrov, Andre (1982), "The world's simplest axiom of choice fails", Manuscripta Mathematica, 38 (3): 325–332, doi:10.1007/BF01170929