Properties

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	κ (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 definable principal congruences	[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)]