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This shows you the differences between two versions of the page.
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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 | ||
| $f '\circ f=g'\circ g$. | $f '\circ f=g'\circ g$. | ||
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