Table of Contents
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]]
