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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>
 +)]
 +
 +
 +