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amalgamation_property [2010/08/20 20:28]
jipsen created
amalgamation_property [2010/08/20 20:30] (current)
jipsen
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A class $\mathcal{K}$ of structures is said to have the A class $\mathcal{K}$ of structures is said to have the
-\emph{amalgamation property} if for every amalgam with  +\emph{amalgamation property} if for every amalgam $\langle \mathbf{A},f,\mathbf{B},g,\mathbf{C}\rangle$ with  
-$\mathbf{A},\mathbf{B},\mathbf{C}\in\mathcal{K}$ and $A\neq\varnothing$+$\mathbf{A},\mathbf{B},\mathbf{C}\in\mathcal{K}$ and $A\neq\emptyset$
there exists a structure $\mathbf{D}\in\mathcal{K}$ and embeddings there exists a structure $\mathbf{D}\in\mathcal{K}$ and embeddings
$f ':\mathbf{B}\to\mathbf{D}$, $g':\mathbf{C}\to\mathbf{D}$ such that $f ':\mathbf{B}\to\mathbf{D}$, $g':\mathbf{C}\to\mathbf{D}$ such that
$f '\circ f=g'\circ g$. $f '\circ f=g'\circ g$.