\bibliographystyle{plain}
\begin{thebibliography}{10}

\bibitem{birkhoff} 
G.~Birkhoff,
{\sl Lattice Theory}, Corrected reprint of the 1967 third
edition, American Mathematical Society Colloquium Publications,
{\bf 25}, American Mathematical Society, Providence, R.I., 1984.

\bibitem{burris-sanka} 
S. Burris and H.P. Sankappanavar, 
{\sl A Course in Universal Algebra}, Graduate Texts in Mathematics
No. 78, Springer--Verlag, 1981.

\bibitem{czedli} 
G.~Cz\'{e}dli,
{\it A Mal'cev type condition for the 
semi-distributivity of congruence lattices}, 
Acta Sci.\ Math.\ {\bf 43} (1981), 267--272.

\bibitem{czedli1} 
G.~Cz\'{e}dli,
{\it A characterization for congruence semi-distributivity}, 
in {\sl Universal Algebra and Lattice Theory},
Springer Lecture Notes in Mathematics {\bf 1004},
1983, 104--110.

\bibitem{czedli2} 
G.~Cz\'{e}dli,
{\it Mal'cev conditions for Horn sentences
with congruence permutability}, 
Acta Math.\ Hung.\  {\bf 44} (1984), 115--124.

\bibitem{czedli-day} 
G.~Cz\'{e}dli and A.~Day,
{\it Horn sentences with ${\rm (W)}$ and weak Mal'cev conditions}, 
Algebra Universalis {\bf 19} (1984), 217--230.

\bibitem{davey-p-r} 
B.~A.~Davey, W.~Poguntke, and I.~Rival, 
{\it A characterization of semi-distributivity},
Algebra Universalis {\bf 5} (1975), 72--75.

\bibitem{day1} 
A.~Day, 
{\it A characterization of modularity
for congruence lattices of algebras}, 
Canad.\ Math.\ Bull.\ {\bf 12} (1969), 167--173.

\bibitem{day2} A.~Day, {\it $p$-Modularity implies modularity
in equational classes}, Algebra Universalis {\bf 3}
(1973), 398--399.

\bibitem{day3} A.~Day, {\it Splitting lattices and congruence modularity},
{\sl Contributions to Universal Algebra}
(Colloq., J\'ozsef Attila Univ., Szeged, 1975), pp. 57--71,
Colloq. Math. Soc. Janos Bolyai {\bf 17}, 
North-Holland, Amsterdam, 1977.

\bibitem{day-freese} A.~Day and R.~Freese, 
{\it A characterization of identities
implying congruence modularity, I},
Canad.\ J.\ Math.\ {\bf 32} (1980), 1140--1167.

\bibitem{day-kiss} 
A.~Day and E.~W.~Kiss, 
{\it Frames and rings in congruence modular varieties},
J.\ Algebra {\bf 109} (1987), 479--507.

\bibitem{dedekind} 
R.~Dedekind,
{\it \"{U}ber die von drei Moduln erzeugte Dualgruppe},
Math.\ Ann.\ {\bf 53} (1900), 371--403.

\bibitem{fajtlowicz-schmidt}
S.~Fajtlowicz and J.~Schmidt, 
{\it B\'{e}zout families, join-congruences, and meet-irreducible ideals},
{\sl Lattice theory} (Proc.\ Colloq., Szeged, 1974), pp.\ 51--76. 
Colloq.\ Math.\ Soc.\ Janos Bolyai, {\bf 14},
North-Holland, Amsterdam, 1976. 

\bibitem{freese1} 
R.~Freese, 
{\it Ideal lattices of lattices},
Pacific J.\ Math.\ {\bf 57} (1975), 125--133.

\bibitem{freese-jezek-nation}
R.~Freese, J.~Jezek, and J.~B.~Nation,
{\sl Free Lattices},
Mathematical Surveys and Monographs {\bf 42},
American Math.\ Soc., 1995.

\bibitem{freese-jonsson} R.~Freese and 
B.~J\'{o}nsson, {\it Congruence modularity implies
the Arguesian identity}, Algebra Universalis {\bf 6}
(1976), 225--228.

\bibitem{freese-kearnes-nation} 
R.~Freese, K.~Kearnes and J.~B.~Nation, 
{\it Congruence lattices of congruence semidistributive algebras}, 
Lattice theory and its applications,
63--78, Res. Exp. Math. {\bf 23}, Heldermann, Lemgo, 1995. 

\bibitem{freese-mckenzie} 
R.~Freese and R.~McKenzie, 
{\sl Commutator Theory for Congruence Modular Varieties}, 
LMS Lecture Notes {\bf 125}, Cambridge University Press, 1987.

\bibitem{freese-nation1} 
R.~Freese and J.~B.~Nation, 
{\it Congruence lattices of semilattices}, 
Pacific J.\ Math. {\bf 49} (1973), 51--58.

%\bibitem{freese-nation2} 
%R.~Freese and J.~B.~Nation, 
%{\it Projective lattices}, 
%Pacific J.\ Math. {\bf 75} (1978), 93--106.

\bibitem{freese-nation2} 
R.~Freese and J.~B.~Nation, 
{\it 3,3 Lattice implications imply 
congruence modularity}, Algebra Universalis {\bf 7}
(1977), 191--194.

\bibitem{fun-nak} 
N.~Funayama and T.~Nakayama,
{\it On the distributivity of a lattice of lattice 
congruences}, Proc.\ Imp.\ Acad.\ Tokyo {\bf 18} (1942), 553--554.

\bibitem{disquisitiones}
C.~F.~Gauss,
{\sl Disquisitiones Arithmeticae}
Lipsiae, in commissis apud Gerh.~Fleischer Jun., 1801.
%Translated and with a preface by Arthur~A.~Clarke.
%Revised by William~C.~Waterhouse, Cornelius~Greither
%and A.~W.~Grootendorst and with a preface by
%Waterhouse. Springer-Verlag, New York, 1986.

\bibitem{garcia-taylor} 
O.~C.~Garc\'{i}a and W.~Taylor, 
{\sl The lattice of interpretability types of varieties},
Mem.\ Amer.\ Math.\ Soc.\ {\bf 50}, 1984.

\bibitem{gorbunov}
V.~A.~Gorbunov, 
{\sl Algebraic Theory of Quasivarieties}, 
Translated from the Russian. 
Siberian School of Algebra and Logic. 
Consultants Bureau, New York, 1998. 

\bibitem{gratzer-schmidt} 
G.~Gr\"atzer and E.~T.~Schmidt,
{\it Characterizations of congruence lattices of abstract algebras},
Acta Sci.\ Math.\ {\bf 24} (1963), 34--59.

%\bibitem{gumm} H.~P.~Gumm, {\it Is there a Mal'cev 
%theory for single algebras?}, 
%Algebra Universalis {\bf 8} (1978), 320--329.

\bibitem{gumm} 
H.~P.~Gumm, {\sl Geometrical Methods in Congruence
Modular Algebras}, Mem.\ Amer.\ Math.\ Soc. {\bf 45}, 1983.

\bibitem{hagemann-herrmann}
J.~Hagemann and C.~Herrmann,
{\it A concrete ideal multiplication for algebraic
systems and its relation to congruence distributivity},
Arch.\ Math. (Basel) {\bf 32} (1979), 234--245.

\bibitem{hagemann-mitschke}
J.~Hagemann and A.~Mitschke, 
{\it On $n$-permutable congruences}, 
Algebra Universalis {\bf 3} (1973), 8--12.
 
\bibitem{haiman_th} 
M.~Haiman, 
{\it Arguesian lattices which are not linear},
Bull.\ Amer.\ Math.\ Soc.\ (N.S.) {\bf 16} (1987), no.\ 1,
121--123.

\bibitem{herrmann} 
C.~Herrmann, 
{\it Affine algebras in congruence modular varieties}, 
Acta Sci.\ Math.\ {\bf 41} (1979), 119--125.

\bibitem{herrmann-poguntke1} 
C.~Herrmann and W.~Poguntke, 
{\it Axiomatic classes of modules}, 
Darmstadt Preprint {\bf 12}, 1972.

\bibitem{herrmann-poguntke2} 
C.~Herrmann and W.~Poguntke, 
{\it The class of sublattices of normal subgroup
lattices is not elementary},
Algebra Universalis {\bf 4} (1974), 280--286.

\bibitem{hobby-mckenzie} 
D.~Hobby and R.~McKenzie, 
{\sl The Structure of Finite Algebras}, 
Contemporary Mathematics v.~76, 
American Mathematical Society, 1988.

\bibitem{hodges} 
W.~Hodges,
{\sl Model Theory}, 
Encyclopedia of Mathematics and its Applications {\bf 42},
Cambridge University Press, Cambridge, 1993.

%\bibitem{hutchinson} G.~Hutchinson,
%{\it On the representation of lattices by modules},
%Trans.\ Amer.\ Math.\ Soc.\ {\bf 209} (1975), 311--351.

\bibitem{hutchinson-czedli} 
G.~Hutchinson and G.~Cz\'{e}dli,
{\it A test for identities satisfied in lattices
of submodules}, 
Algebra Universalis {\bf 8} (1978), 269--309.

\bibitem{jonsson0} 
B.~J\'{o}nsson,
{\it Modular lattices and Desargues' Theorem},
Math.\ Scand.\ 2 (1954), 295--314.

\bibitem{jonsson1} 
B.~J\'{o}nsson,
{\it Algebras whose congruence lattices are distributive},
Math.\ Scand.\ 21 (1967), 110--121.

\bibitem{jonsson2} 
B.~J\'{o}nsson, 
{\it Identities in congruence varieties}, 
{\sl Lattice theory} (Proc.\ Colloq., Szeged, 1974), 
pp. 195--205, Colloq.\ Math.\ Soc.\ Janos Bolyai, {\bf 14}, 
North-Holland, Amsterdam, 1976.

\bibitem{jonsson3} 
B.~J\'{o}nsson, 
{\it Congruence varieties},
Algebra Universalis {\bf 10} (1980), 355--394.

\bibitem{jonsson-rival} 
B.~J\'{o}nsson and I.~Rival,
{\it Lattice varieties covering the smallest nonmodular variety},
Pacific J.\ Math.\ {\bf 82} (1979), 463--478. 

\bibitem{kaarli-mckenzie} 
K.~Kaarli and R.~McKenzie,
{\it Affine complete varieties are congruence distributive},
Algebra Universalis {\bf 38} (1997), 329--354.

\bibitem{kaarli-pixley} 
K.~Kaarli and A.~Pixley,
{\it Affine complete varieties},
Algebra Universalis {\bf 24} (1987), 74--90.

\bibitem{sym} 
K.~A.~Kearnes, 
{\it An order-theoretic property of the commutator}, 
Internat.\ J.\ Algebra Comput.\ {\bf 3} (1993), 491--533.

%\bibitem{semi} K.~A.~Kearnes, {\it Semilattice modes I\& II},
%Algebra Universalis {\bf 34} (1995), 220--272, 273--303.

\bibitem{diff} 
K.~A.~Kearnes,
{\it Varieties with a difference term}, 
J.\ Algebra {\bf 177} (1995), 926--960.

%\bibitem{rs} K.~A.~Kearnes, 
%{\it Residual smallness restricted to congruence types, II},
%manuscript (1996).

\bibitem{congid} 
K.~A.~Kearnes, 
{\it A characterization of locally finite varieties 
that satisfy a nontrivial congruence identity}, 
Algebra Universalis  {\bf 42} (1999), 195--204.

\bibitem{idem} 
K.~A.~Kearnes, 
{\it Almost all minimal
idempotent varieties are congruence modular}, 
Algebra Universalis {\bf 44} (2000), 39--45.

\bibitem{sdj} 
K.~A.~Kearnes, 
{\it Congruence semidistributivity is equivalent to a
congruence identity},
Algebra Universalis  {\bf 46}  (2001), 373--387. 

\bibitem{k-kiss} 
K.~A.~Kearnes and E.~W.~Kiss,
{\it Finite algebras of finite complexity},
Discrete Math.\ {\bf 207} (1999), 89--135.

\bibitem{k-kiss2} 
K.~A.~Kearnes and E.~W.~Kiss,
{\it The triangular principle is equivalent to the triangular scheme}, 
Algebra Universalis {\bf 54} (2005), no. 3, 273--283.

\bibitem{k-nation}
K.~A.~Kearnes and J.~B.~Nation,
{\it Axiomatizable and nonaxiomatizable congruence prevarieties.} 
Algebra Universalis {\bf 59} (2008), no. 3-4, 323--335. 

%\bibitem{k-szendrei1} K.~A.~Kearnes and 
%\'{A}.~Szendrei, {\it Self-rectangulating varieties of type
%{\bf 5}}, Internat.\ J.\ Algebra Comput.\ {\bf 7} (1997), 511--540.

\bibitem{k-szendrei2} 
K.~A.~Kearnes and \'{A}.~Szendrei, 
{\it The relationship between two commutators}, 
Internat.\ J.\ Algebra Comput.\ {\bf 8}
(1998), 497--531.

%\bibitem{k-szendrei3} K.~A.~Kearnes and 
%\'{A}.~Szendrei, {\it The residual character of strictly 
%simple term minimal algebras},
%Algebra Universalis {\bf 42} (1999), 269--292.

\bibitem{k-valeriote} 
K.~A.~Kearnes and M.~A.~Valeriote, 
{\it A modification of Polin's variety},
Algebra Universalis {\bf 41} (1999), 229--231.

\bibitem{kiss-prohle} 
E.~W.~Kiss and P.~Pr\H{o}hle,
{\it Problems and results in tame congruence theory},
Algebra Universalis {\bf 29} (1992), 151--171.

%\bibitem{kostinsky} 
%A.~Kostinsky, 
%{\it Projective lattices and bounded homomorphisms},
%Pacific J.\ Math.\ {\bf 40} (1972), 111--119.

\bibitem{lip1} 
P.~Lipparini, {\it Congruence identities satisfied in 
$n$-permutable varieties},  
Boll.\ Un.\ Mat.\ Ital.\ B (7) 8 (1994), no.\ 4, 851--868.

\bibitem{lipparini3} 
P.~Lipparini,
{\it Commutator theory without join-distributivity},
Trans.\ Amer.\ Math.\ Soc.\ {\bf 346} (1994), 177--202.

\bibitem{lipparini1} 
P.~Lipparini, 
{\it $n$-permutable varieties satisfy nontrivial congruence identities},
Algebra Universalis {\bf 33} (1995), 159--168.

\bibitem{lipparini2} 
P.~Lipparini, 
{\it A characterization of varieties with a difference term},
Canad.\ Math.\ Bull.\ {\bf 39} (1996), 308--315.

\bibitem{lipparini4} 
P.~Lipparini, 
{\it A characterization of varieties with a difference term, II:
neutral = meet semi-distributive},
Canad.\ Math.\ Bull.\ {\bf 41} (1998), 318--327.

\bibitem{lip3} 
P.~Lipparini, 
{\it  A new proof that $n$-permutable varieties satisfy lattice identities}, 
manuscript available at \hfill\hfill \linebreak
{\tt http://www.mat.uniroma2.it/\~{}lipparin/nperm2.dvi}

\bibitem{lip4} 
P.~Lipparini, 
{\it Every m-permutable variety satisfies the 
congruence identity $ \alpha \beta_h= \alpha \gamma_h$},
to appear in Proc.\ Amer.\ Math.\ Soc.\

\bibitem{maltsev} 
A.~I.~Maltsev, 
{\it On the general theory of algebraic systems {\rm (in
Russian)}}, Mat.\ Sb.\ N.\ S.\ {\bf 35}(77) (1954), 3--20.

\bibitem{maclane} 
S.~Mac Lane,
{\sl Categories for the Working Mathematician},
Second edition, Graduate Texts in Mathematics
{\bf 5}, Springer--Verlag, 1998. 

\bibitem{mckenzie1} 
R.~McKenzie, 
{\it Equational bases and nonmodular lattice 
varieties}, Trans.\ Amer.\ Math.\ Soc.\ {\bf 174}
(1972), 1--43.

\bibitem{mckenzie2} 
R.~McKenzie, 
{\it Some unsolved problems between 
lattice theory and equational logic}, 
Proceedings of the University of Houston 
Lattice Theory Conference (Houston, Tex., 1973), pp. 564--573,
Dept.\ Math., Univ.\ Houston, Houston, Tex., 1973.

\bibitem{mckenzie3} 
R.~McKenzie, 
{\it Finite forbidden lattices},
in {\sl Universal Algebra and Lattice Theory},
Lecture Notes in Mathematics {\bf 1004},
Springer-Verlag, 1983.

\bibitem{mmt} 
R.~McKenzie, G.~McNulty, and W.~Taylor,
{\sl Algebras, Lattices, Varieties, Volume I},
The Wadsworth \& Brooks/Cole Mathematics Series. 
Wadsworth \& Brooks/Cole Advanced Books \& Software, 
Monterey, CA, 1987.

\bibitem{mederly} P.~Mederly, {\it Three Mal'cev
type theorems and their application},
Mat.\ \v{C}asopis Sloven.\ Akad.\ Vied {\bf 25} (1975), 83--95.

\bibitem{nation} 
J.~B.~Nation, 
{\it Varieties whose congruence lattices satisfy
certain identities}, Algebra Universalis {\bf 4} (1974), 78--88.

%\bibitem{nation2} J.~B.~Nation, 
%{\it Finite sublattices of a free lattice}, 
%Trans. Amer. Math. Soc. {\bf 269} (1982), 311--337.

\bibitem{newrly-valeriote} 
N.~Newrly and M.~A.~Valeriote, 
{\it Some generalizations of Polin's variety}, 
manuscript, 1999.

\bibitem{p3-szabo} P.~P.~P\'{a}lfy and
C.~Szab\'{o}, {\it Congruence varieties of groups and abelian
groups}, Lattice theory and its applications 
(Darmstadt, 1991), 163--183, Res.\ Exp.\ Math.\ {\bf 23}
Heldermann, Lemgo, 1995. 

\bibitem{pixley1} 
A.~Pixley,
{\it Distributivity and permutability of congruence
relations in equational classes of algebras},
Proc.\ Amer.\ Math.\ Soc.\ {\bf 14} (1963), 105--109.

\bibitem{pixley2} 
A.~Pixley,
{\it Local Mal'cev conditions}, 
Canad.\ Math.\ Bull.\ {\bf 15}
(1972), 559--568.

\bibitem{polin} 
S.~V.~Polin, 
{\it Identities in congruence lattices of universal algebras},
Mat.\ Zametki {\bf 22} (1977), 443--451. 

\bibitem{smith} 
J.~D.~H.~Smith,
{\sl Mal'cev Varieties}, 
Lecture Notes in Mathematics {\bf 554},
Springer-Verlag, 1976.

\bibitem{taylor1} 
W.~Taylor, 
{\it Characterizing Mal'cev conditions}, 
Algebra Universalis {\bf 3} (1973), 351--397.

\bibitem{taylor3} 
W.~Taylor, 
{\it Varieties obeying homotopy laws}, 
Canadian J.\ Math.\ {\bf 29}
(1977), 498--527.

%\bibitem{taylor2} 
%W.~Taylor, {\it Some 
%applications of the term condition}, 
%Algebra Universalis {\bf 14} (1982), 11--24.

%\bibitem{finbas}
%R.~Willard, 
%{\it A finite basis theorem for residually finite, congruence
%meet-semidistributive varieties},  
%J.\ Symbolic Logic  {\bf 65}  (2000),  187--200. 

\bibitem{wille} 
R.~Wille, 
{\sl Kongruenzklassengeometrien}, 
Lecture Notes in Mathematics {\bf 113},
Springer-Verlag, 
%Berlin, 
1970.

\end{thebibliography}
