### 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]]