PlanetMath: universal structure

(more info)

Math for the people, by the people.

Main Menu

universal structure

(Definition)

Let be a first order language, and let be an elementary class of -structures. Let $\kappa$ be a cardinal. $R_{\kappa}$ be the set of structures from with cardinality less than or equal to $\kappa$ .

Let $M \in R_{\kappa}$ . Suppose that for every $N \in R_{\kappa}$ there is an embedding of into . Then we say is universal.

"universal structure" is owned by Timmy.

(view preamble)

Also defines:

universal

Keywords:

embedding

Log in to rate this entry.
(view current ratings)

Cross-references: embedding, cardinality, structures, cardinal, elementary class, first order language
There are 3 references to this entry.

This is version 1 of universal structure, born on 2003-01-24.
Object id is 3922, canonical name is UniversalStructure.
Accessed 4641 times total.

Classification:

AMS MSC:	03C50 (Mathematical logic and foundations :: Model theory :: Models with special properties )
	03C52 (Mathematical logic and foundations :: Model theory :: Properties of classes of models)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact