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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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### Models 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.

### Course 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 ...

### Finite 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 ...

### Encyclopaedia of Mathematics, Supplement III (2001)

by Michiel Hazewinkel

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

## Online dictionaries and encyclopedias with entries for Ultraproduct

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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.