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Ultraproduct

Definition of the noun Ultraproduct

What does Ultraproduct mean as a name of something?

noun

  1. [mathematics] A quotient of the direct product of a family of structures

Explanation

The ultraproduct is a mathematical construction that appears mainly in abstract algebra and in model theory, a branch of mathematical logic. An ultraproduct is a quotient 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 factors are equal.

Printed encyclopedias and other books with definitions for Ultraproduct

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Google previewModels and Games (2011)

by Jouko Väänänen

An ultraproduct is a way to combine a set A of models into one single model in such a way that the new model has all the first-order properties that "most" of the models in A have. A variety of results 6.70 Ultraproducts 119 Ultraproducts.

Google previewCourse of Mathematical Logic (2012)

Volume 2 Model Theory by R. Fraïssé

Then the ultraproduct is a multirelation whose base is a singleton, which cannot be logically equivalent to any R. 7.1.3. Any maximal ultrapower of a multirelation R is a logical extension of R. P Recall that in an ultrapower all the multirelations ...

Google previewFinite and Algorithmic Model Theory (2011)

by Javier Esparza, Christian Michaux, Charles Steinhorn

Indeed, an ultraproduct is a vertex transitive graph of valency d, and all such are well-known to be strongly minimal; see for example [8], Lemma 2.2.11. Example 4.3.9 Lastly, let M be a smoothly approximable structure — see Section 4.4 ...

Google previewEncyclopaedia of Mathematics, Supplement III (2001)

by Michiel Hazewinkel

COMPACT SUBGROUP climbing search see; hill- — closed see; ultraproduct 478 486.pdf.

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Video about Ultraproduct

Ultraproduct Meaning

Video shows what ultraproduct means. A quotient of the direct product of a family of structures. Ultraproduct Meaning. How to pronounce, definition audio ...

Scrabble value of U1L1T1R1A1P3R1O1D2U1C3T1

The value of this 12-letter word is 17 points, but it's not an accepted word in the Official Scrabble Players Dictionary.

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