joint embedding property
Let be a class of models (structures) of a given signature. We say that has the joint embedding property (abbreviated JEP) iff for any models and in there exists a model in such that both and are embeddable in . [1, 2]
Examples include :
The class of all groups.
The class of all monoids.
The class of all non-trivial Boolean algebras.
As is the case with the above examples, classes having the joint embedding property often satisfy an even stronger condition - for every indexed family of models in the class there is a model in the class into which each member of the family can be embedded. This is known as the strong joint embedding property (abbreviated SJEP). 
Elementary classes with the joint embedding property may be characterized syntactically and semantically:
- 1 Abraham Robinson: Forcing in model theory, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 245-250
- 2 Colin Naturman, Henry Rose: Ultra-universal models, Quaestiones Mathematicae, 15(2), 1992, 189-195
- 3 Colin Naturman: Interior Algebras and Topology, Ph.D. thesis, University of Cape Town Department of Mathematics, 1991
|Title||joint embedding property|
|Date of creation||2013-03-22 19:36:14|
|Last modified on||2013-03-22 19:36:14|
|Last modified by||Naturman (26369)|
|Defines||joint embedding property|
|Defines||strong joint embedding property|