Some common first-order theories ordered by interpretability



The source.

The abbreviations in alphabetical order:

1.AGrp AbelianGroups(+,0,-)
2.BA BooleanAlgebras(v,0,^,1,~)
3.BCK BCKAlgebras(->1)
4.BMod RBooleanModules(v,0,^,1,~,(r in R))
5.BMon BooleanMonoids(v,0,^,1,~,*,e)
6.BRng BooleanRings(+,0,*,1)
7.Band Bands(*)
8.BdLatBoundedLattices(v,0,^,1)
9.BdRL BoundedResiduatedLattices(v,0,^,1,*,e,\,/)
10.BinO Groupoids(*)
11.Brow BrowerianAlgebras(v,^,*,1,->)
12.CA CylindricAlgebras(v,0,^,1,~,c_i,d_ij)
13.CURngCommutativeRingsWithUnit(+,0,-,*,1)
14.Chn Chains(<=)
15.DG Digraphs(E)
16.DGA DigraphAlgebras(*)
17.EquA EquivalenceAlgebras(*)
18.FVec FVectorSpaces(+,0,-,(a in F))
19.Fld Fields(+,0,-,*,1,/)
20.Grp Groups(*,e,^-1)
21.HA HeytingAlgebras(v,0,^,1,->)
22.HO Hoops(*,1,->)
23.ISGrp InverseSemigroups(*,^-1)
24.JSLatJoinSemilattices
25.KA KleeneAlgebras(v,0,*,1,~)
26.LGrp LatticeOrderedGroups(v,^,*,^-1,e)
27.LLA LinearLogicAlgebras(v,0,^,1,+,d,*,e,->)
28.LRIM Polrims(*,1,-><=)
29.Lat Lattices(v,^)
30.Loop Loops(*,e,\,/)
31.MA ModalAlgebras(v,0,^,1,~,<>,[])
32.MSLatMeetSemilattices
33.MVA MVAlgebras(v,0,^,1,*,->)
34.Mon Monoids(*,e)
35.OFld OrderedFields(+,0,-,*,1,/,<=)
36.OrdA OrderAlgebras(*)
37.PO Posets(<=)
38.QGrp Quasigroups(*,\,/,e)
39.RA RelationAlgebras(v,0,^,1,~,*,e,^-1)
40.RL ResiduatedLattices(v,^,*,e,\,/)
41.RMod RModules(+,0,-,(r in R))
42.Rng Rings(+,0,-,*)
43.SGrp Semigroups(*)
44.SLat Semilattices(*)
45.Shl Shells(+,0,*,1)
46.TA TenseAlgebras(v,0,^,1,~,<f><p>)
47.Tour Tournaments(*)
48.URng RingsWithUnit(+,0,-,*,1)