This page lists all the properties and their possible values that are currently part of some entry in this database.
Click on a property to get a brief explanation.
(Available soon) Click on the value of a property to see all classes that mention this property with the selected value.
| Classtype | variety, quasivariety, universal class, first-order class, second-order class, higher-order class |
|---|---|
| Equational theory | decidable (PTIME, NPTIME, PSPACE, EXPTIME,…), undecidable, unspecified (so far) |
| Quasiequational theory | decidable (PTIME, NPTIME, PSPACE, EXPTIME,…), undecidable, unspecified (so far) |
| First-order theory | decidable (PTIME, NPTIME, PSPACE, EXPTIME,…), undecidable, unspecified (so far) |
| Locally finite | yes, no, unspecified (so far) |
| Residual size | $\kappa$ (cardinality), finite, unbounded |
| Congruence distributive | yes, no, unspecified (so far) |
| Congruence modular | yes, no, unspecified (so far) |
| Congruence n-permutable | yes $n=?$, no, unspecified (so far) |
| Congruence regular | yes, no, unspecified (so far) |
| Congruence e-regular | yes, no, unspecified (so far) |
| Congruence uniform | yes, no, unspecified (so far) |
| Congruence types | permutational (1), abelian (2), Boolean (3), lattice (4), semilattice (5) |
| Congruence extension property | yes, no, unspecified (so far) |
| Definable principal congruences | yes, no, unspecified (so far) |
| Equationally def. pr. cong. | yes, no, unspecified (so far) |
| Amalgamation property | yes, no, unspecified (so far) |
| Strong amalgamation property | yes, no, unspecified (so far) |
| Epimorphisms are surjective | yes, no, unspecified (so far) |