##  [Amalgamation Property](/index.php/amalgamation-property) 

  ##  [Amalgamation Property](https://mathlogic.quantumdictionary.io/amalgamation-property-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/index.php/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A property of a class of structures meaning that any two structures in the class that share a common substructure can be embedded into a single structure from the class in such a way that the two embeddings agree on the common substructure (they are amalgamated).

 

 

 

 

 





 

 



 ##  [Amalgamation Property](https://algebra.quantumdictionary.io/amalgamation-property-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A class of structures (often a variety or a model class) has the amalgamation property (AP) when any pair of embeddings of a common substructure into two structures can be jointly embedded into a single superstructure so that the two embeddings agree on the common part (there exists an amalgam or pushout for the diagram of embeddings).