A *relation algebra* is a structure ** A** = (

(*A*,∨,0,
∧,1,¬) is a Boolean algebra,

(*A*,o,*e*) is a monoid,

o is *join-preserving*:
(*x*∨*y*)o*z* = (*x*o*z*)∨(*y*o*z*)

^{∪} is an *involution*:
*x*^{∪}^{∪} = *x* and (*x*o*y*)^{∪} = *y*^{∪}o*x*^{∪}

^{∪} is *join-preserving*:
(*x*∨*y*)^{∪} = *x*^{∪}∨*y*^{∪}

o is residuated: *x*^{∪}o(¬(*x*o*y*)) ≤ ¬*y*.

Let ** A** and

Classtype | variety |

Equational theory | undecidable |

Quasiequational theory | undecidable |

First-order theory | undecidable |

Locally finite | no |

Residual size | unbounded |

Congruence distributive | yes |

Congruence modular | yes |

Congruence n-permutable | yes, n = 2 |

Congruence regular | yes |

Congruence uniform | yes |

Congruence extension property | yes |

Definable principal congruences | yes |

Equationally definable principal congruences | yes |

[Discriminator variety]? | yes |

Amalgamation property | no |

Strong amalgamation property | no |

Epimorphisms are surjective | no |

[Size 1]?: 1

[Size 2]?: 1

[Size 3]?: 0

[Size 4]?: 3

[Size 5]?: 0

[Size 6]?: 0

[Representable relation algebras]?

[Commutative relation algebras]?

[Square-increasing relation algebras]?

[Semiassociative relation algebras]?