# Ultraproduct

On this page:

- Definition of the noun Ultraproduct
- Explanation
- Printed encyclopedias and other books with definitions for Ultraproduct
- Online dictionaries and encyclopedias with entries for Ultraproduct
- Video about Ultraproduct
- Scrabble value of U
_{1}L_{1}T_{1}R_{1}A_{1}P_{3}R_{1}O_{1}D_{2}U_{1}C_{3}T_{1} - Share this page

## Definition of the noun Ultraproduct

What does Ultraproduct mean as a name of something?

**noun**

- [
*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

Click on a title to look inside that book (if available):

### 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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## 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 U_{1}L_{1}T_{1}R_{1}A_{1}P_{3}R_{1}O_{1}D_{2}U_{1}C_{3}T_{1}

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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