properties - MathStructures

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=====Properties=====

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]]                                    |[[varieties|variety]], [[quasivarieties|quasivariety]], [[universal classes|universal class]], [[first-order classes|first-order class]], [[second-order classes|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) |

Trace: • jordan_algebras • symmetric_relations • directed_graphs • relativized_relation_algebras • cancellative_commutative_monoids • multiplicative_lattices • first-order_classes • lattices • finite_semilattices_with_identity • finite_ordered_semigroups