amalgamation property


A class of L-structuresMathworldPlanetmath S has the amalgamation property if and only if whenever A,B1,B2S and fi:ABi are elementary embeddings for i{1,2} then there is some CS and some elementary embeddings gi:BiC for i{1,2} so that g1(f1(x))=g2(f2(x)) for all xA. That is, the following diagram commutes.

\xymatrix&A\ar[dl]f1\ar[dr]f2&B1\ar[dr]g1&&B2\ar[dl]g2&C&

Compare this with the free product with amalgamated subgroup for groups and the definition of pushout there.

Title amalgamation property
Canonical name AmalgamationProperty
Date of creation 2013-03-22 13:25:01
Last modified on 2013-03-22 13:25:01
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 8
Author Mathprof (13753)
Entry type Definition
Classification msc 03C52
Related topic FreeProductWithAmalgamatedSubgroup
Related topic Confluence
Related topic JointEmbeddingProperty
Defines amalgamation property