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Ultraproduct

The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is the quotient set of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of this construction in which all…

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Overview

Definition

Examples

Łoś's theorem

Direct limits of ultrapowers (ultralimits)

Ultraproduct monad

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Map overview Semantic statistics

Ultraproduct

Nodes57
Edges56
Triples44
Avg. degree1.96
Density0.035088
Components1

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Ultraproduct

Top relations

related to References · 15
Ultraproduct → Alan, An Introduction, Bell, Burris, Course, Dover Publications, ISBN, John Lane, Millennium, Models, Sankappanavar, Slomson, Stanley, Ultraproducts, Universal Algebra
related to Ultrapower · 6
Ultraproduct → An, Cartesian, Explicitly, For, The, This
related to Ultraproduct monad · 6
Ultraproduct → Explicitly, Fam, FinFam, Similarly, So, The
related to Łoś's theorem · 5
Ultraproduct → It, Jerzy, Let, More, Then
is a · 4
Ultraproduct → mathematical construction that appears mainly in abstract algebra and mathematical logic, quotient set of the direct product of a family of structures, set of all U, set of equivalence classes thus generated.Finitary operations on the Cartesian product
related to Definition · 4
Ultraproduct → Cartesian, For, The, This
related to Examples · 4
Ultraproduct → Analogously, For, The, Their

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Important terminology

displaystyle mathcal set ultrafilter ultrapower prod limits left right textstyle theorem product index every example equivalence construction bullet one number

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ultraproductis amathematical construction that appears mainly in abstract algebra and mathematical logic0.90text
Ultraproductis aquotient set of the direct product of a family of structures0.90text
Ultraproductis aset of all U0.90text
Ultraproductis aset of equivalence classes thus generated.Finitary operations on the Cartesian product0.90text
Ultraproductrelated to DefinitionThe0.60section
Ultraproductrelated to DefinitionFor0.60section
Ultraproductrelated to DefinitionCartesian0.60section
Ultraproductrelated to DefinitionThis0.60section
Ultraproductrelated to ExamplesThe0.60section
Ultraproductrelated to ExamplesTheir0.60section
Ultraproductrelated to ExamplesFor0.60section
Ultraproductrelated to ExamplesAnalogously0.60section

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    Min side: 3
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