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- Q17101965 subject Q7451685.
- Q17101965 abstract "In universal algebra and model theory, a class of structures K is said to have the joint embedding property if for all structures A and B in K, there is a structure C in K such that both A and B have embeddings into C.It is one of the three properties used to define the age of a structure.A similar but different notion to the joint embedding property is the amalgamation property. To see the difference, first consider the class K (or simply the set) containing three models with linear orders, L1 of size one, L2 of size two, and L3 of size three. This class K has the joint embedding property because all three models can be embedded into L3. However, K does not have the amalgamation property. The counterexample for this starts with L1 containing a single element e and extends in two different ways to L3, one in which e is the smallest and the other in which e is the largest. Now any common model with an embedding from these two extensions must be at least of size five so that there are two elements on either side of e.Now consider the class of algebraically closed fields. This class has the amalgamation property since any two field extensions of a prime field can be embedded into a common field. However, two arbitrary fields cannot be embedded into a common field when the characteristic of the fields differ.".
- Q17101965 wikiPageWikiLink Q1047547.
- Q17101965 wikiPageWikiLink Q1636734.
- Q17101965 wikiPageWikiLink Q1851710.
- Q17101965 wikiPageWikiLink Q369377.
- Q17101965 wikiPageWikiLink Q467606.
- Q17101965 wikiPageWikiLink Q4691833.
- Q17101965 wikiPageWikiLink Q4739384.
- Q17101965 wikiPageWikiLink Q7451685.
- Q17101965 wikiPageWikiLink Q836088.
- Q17101965 wikiPageWikiLink Q912887.
- Q17101965 wikiPageWikiLink Q980509.
- Q17101965 comment "In universal algebra and model theory, a class of structures K is said to have the joint embedding property if for all structures A and B in K, there is a structure C in K such that both A and B have embeddings into C.It is one of the three properties used to define the age of a structure.A similar but different notion to the joint embedding property is the amalgamation property.".
- Q17101965 label "Joint embedding property".