Some common first-order theories ordered by interpretability



The source.

The abbreviations in alphabetical order:

.AGrp AbelianGroups(+,0,-)
.BA BooleanAlgebras(v,0,^,1,~)
.BCK BCKAlgebras(->1)
.BMod RBooleanModules(v,0,^,1,~,(r in R))
.BMon BooleanMonoids(v,0,^,1,~,*,e)
.BRng BooleanRings(+,0,*,1)
.Band Bands(*)
.BdLatBoundedLattices(v,0,^,1)
.BdRL BoundedResiduatedLattices(v,0,^,1,*,e,\,/)
.BinO Groupoids(*)
.Brow BrowerianAlgebras(v,^,*,1,->)
.CA CylindricAlgebras(v,0,^,1,~,c_i,d_ij)
.CURngCommutativeRingsWithUnit(+,0,-,*,1)
.Chn Chains(<=)
.DG Digraphs(E)
.DGA DigraphAlgebras(*)
.EquA EquivalenceAlgebras(*)
.FVec FVectorSpaces(+,0,-,(a in F))
.Fld Fields(+,0,-,*,1,/)
.Grp Groups(*,e,^-1)
.HA HeytingAlgebras(v,0,^,1,->)
.HO Hoops(*,1,->)
.ISGrp InverseSemigroups(*,^-1)
.JSLatJoinSemilattices
.KA KleeneAlgebras(v,0,*,1,~)
.LGrp LatticeOrderedGroups(v,^,*,^-1,e)
.LLA LinearLogicAlgebras(v,0,^,1,+,d,*,e,->)
.LRIM Polrims(*,1,-><=)
.Lat Lattices(v,^)
.Loop Loops(*,e,\,/)
.MA ModalAlgebras(v,0,^,1,~,<>,[])
.MSLatMeetSemilattices
.MVA MVAlgebras(v,0,^,1,*,->)
.Mon Monoids(*,e)
.OFld OrderedFields(+,0,-,*,1,/,<=)
.OrdA OrderAlgebras(*)
.PO Posets(<=)
.QGrp Quasigroups(*,\,/,e)
.RA RelationAlgebras(v,0,^,1,~,*,e,^-1)
.RL ResiduatedLattices(v,^,*,e,\,/)
.RMod RModules(+,0,-,(r in R))
.Rng Rings(+,0,-,*)
.SGrp Semigroups(*)
.SLat Semilattices(*)
.Shl Shells(+,0,*,1)
.TA TenseAlgebras(v,0,^,1,~,<f><p>)
.Tour Tournaments(*)
.URng RingsWithUnit(+,0,-,*,1)