=====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> )]