# Differences

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sets [2010/07/29 15:46] (current)
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+=====Sets=====
+
+Abbreviation: **Set**
+====Definition====
+A \emph{set} is a structure $\mathbf{A}=\langle A\rangle$ with no operations or relations defined on $A$.
+
+==Morphisms==
+Let $\mathbf{A}$ and $\mathbf{B}$ be sets. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$.
+
+====Examples====
+Example 1:
+
+====Basic results====
+
+
+====Properties====
+^[[Classtype]]  |  variety |
+^[[Equational theory]]  |  decidable |
+^[[Quasiequational theory]]  |  decidable |
+^[[First-order theory]]  |  decidable |
+^[[Locally finite]]  |  yes |
+^[[Residual size]]  |  2 |
+^[[Congruence distributive]]  |  no |
+^[[Congruence modular]]  |  no |
+^[[Congruence n-permutable]]  |  no |
+^[[Congruence regular]]  |  no |
+^[[Congruence uniform]]  |  no |
+^[[Congruence extension property]]  |  yes |
+^[[Definable principal congruences]]  |  yes |
+^[[Equationally def. pr. cong.]]  |  no |
+^[[Amalgamation property]]  |  yes |
+^[[Strong amalgamation property]]  |  yes |
+^[[Epimorphisms are surjective]]  |  yes |
+====Finite members====
+
+$\begin{array}{lr} + f(n)= &1\\ +\end{array}$
+
+====Subclasses====
+  [[One-element structures]]
+
+====Superclasses====
+
+====References====
+
+[(Ln19xx>
+)]
+
+
+

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