# Bibliography

#### Fields of Interest

Algebra and Logic

#### Edited Volumes and Monographs

*Order, Algebra, and Logic*, Special Issue of the Journal of Logic and Computation, Volume 20 (Issue 4), 2010 (edited with G. Metcalfe).*Proceedings of the 7th Panhellenic Logic Symposium*, Patras University Press, 2009 (edited with C. Drossos and P. Peppas).*Modern Algebra and Its Applications*, Theoretical Computer Science, Volume 249 (Number 1), 2000 (edited with K. Keimel and M. Mislove).*Ordered Algebraic Structures*, Lecture Notes in Pure and Applied Math., No. 99, Marcel Dekker, 1985 (edited with W. B. Powell).*Residuated Structures in Algebra and Logic*(title tentative) (with George Metcalfe, and Francesco Paoli), in preparation.

#### Articles

*Strong simplicity and states in ordered algebras: Pushing the limits*(with Michal Botur and Jan Kühr), in preparation.*The Archimedean property: New horizons and perspectives*(with Antonio Ledda and Francesco Paoli), submitted for publication.*Join-completions of ordered algebras*(with José Gil-Férez, Luca Spada and Hongjun Zhou), submitted for publication.*Recognizability in residuated lattices*(with José Gil-Férez), to appear in Studia Logica.*Uniform interpolation and compact congruences*(with Samuel van Gool and George Metcalfe), Annals of Pure and Applied Logic 168 (2017), 1927-1948.*Hulls of Ordered Algebras: Projectability, Strong Projectability and Lateral Completeness*(with José Gil-Férez and Antonio Ledda), J. Algebra 483 (2017), 429-474.*Density revisited*(with George Metcalfe), Soft Computing 21(1) (2017), 175-188.*Projectable l-groups and algebras of logic: categorical and algebraic connections*(with José Gil-Férez, Antonio Ledda and Francesco Paoli), Journal of Pure and Applied Algebra 220 (10) (2016), 3514-3532.*The Conrad Program: From l-groups to algebras of logic*(with Michal Botur, Jan Kühr and Lianzhen Liu), J. Algebra 450 (2016), 173-203.*The failure of amalgamation property for semilinear varieties of residuated lattices*(with José Gil-Férez and Antonio Ledda), Math Slovaca 65(4) (2015), 817-828.*Free objects and free extensions in the category of frames*, Math Slovaca 65(2) (2015), 1-8.*Semi-linear varieties of lattice-ordered algebras*(with Antonio Ledda and Francesco Paoli) (F. Montagna, Editor), Trends in Logic, Outstanding Contributions to Logic 6 (2015), 207-221.*Lattice-theoretic properties of algebras of logic*(with Antonio Ledda and Francesco Paoli), Journal of Pure and Applied Algebra 218 (10) (2014), 1932-1952.*Amalgamation and interpolation in ordered algebras*(with George Metcalfe and Franco Montagna), J. Algebra 402 (2014), 21-82.*On Birkhoff’s “common abstraction” problem*(with Francesco Paoli), Studia Logica 100(6) (2012), 1079-1105.*Ordered algebras and logic*(with George Metcalfe and Francesco Paoli), Probability, Uncertainty and Rationality (H. Hosni and F. Montagna, Editors), Publications of the Scuola Normale Superiore di Pisa, Volume 10 (2010), 1-85.*Ordered groups with a conucleus*(with Franco Montagna), Journal of Pure and Applied Algebra 214 (1) (2010), 71-88.*Ordinal decompositions for preordered root systems*(with James Hart), Annals of Pure and Applied Logic 161 (2) (2009), 203-211.*Consequence relations: an order-theoretic and catagorical perspective*(with Nikolaos Galatos), J. Symbolic Logic 74 (3) (2009), 780-810.*Godel incompleteness in AF C*-algebras*(with Daniele Mundici), Forum Math 20 (6) (2008), 1071–1084.*The duality between algebraic posets and bialgebraic frames: a lattice theoretic perspective*(with James Hart), Revista de la Unión Matemática Argentina 49 (1) (2008), 83-98.*Perfect GMV-algebras*(with Antonio Di Nola and Anatolij Dvurecenskij), Communications in Algebra 36 (4) (2008), 1221-1249.*Ordered groups with a modality*(with Franco Montagna), Journal of Pure and Applied Algebra 211 (2007), 511-531. [Note: This article has been retracted at the request of the Editor-in-Chief and authors. Due to an unfortunate oversight by the publisher, the unrevised and incomplete version of the authors’ paper was published. The revised article has been published as: “Ordered groups with a conucleus, Journal of Pure and Applied Algebra 214 (1) (2010), 71-88.”; see above.]*A concrete realization of the Hoare powerdomain*(with James B. Hart), Soft Computing 11 (11) (2007), 1059-1063.*Minimal varieties of involutive residuated lattices*(with Annika Wille), Studia Logica 83 (2006), 401-417.*Generalized MV-algebras*(with N. Galatos), J. Algebra 283(1) (2005), 254-291.*Products of classes of residuated structures*(with Bjarni Jonnson), Studia Logica 77 (2004), 267-292.*Cancellative residuated lattices*(with P. Bahls, J. Cole, N. Galatos and Peter Jipsen), Algebra Universal. 50 (1), (2003), 83-106.*Order algebras as models of linear logic*(with Han Zhang), Studia Logica 76 (2004), 195-219.*The Structure of residuated lattices*(with K. Blount), Internat. J. Algebra Comput. 13(4) (2003), 437–461.*A survey of residuated lattices*(with P. Jipsen), Ordered Algebraic Structures (J. Martinez, editor), Kluwer Academic Publishers, Dordrecht, 2002, 19-56.*Groupable lattices*, Communications in Algebra 23(13) (1995), 4737-4748.*The finite basis theorem for relatively normal lattices*(with J. T. Snodgrass), Algebra Universalis 33 (1995), 40-67.*Decompositions for relatively normal lattices*(with J. B. Hart), Trans. Amer. Math. Soc. 341 (1994), 519-548.*Relation algebras as residuated Boolean algebras*(with B. Jónsson), Algebra Universalis 30 (1993), 469-478*Finite-valued algebraic lattices*(with J. T. Snodgrass), Algebra Universalis 30 (1993), 311-318.*Vector lattices over subfields of the reals*(with P. Bixler, P. Conrad, and W. B. Powell), J. Austral. Math. Soc. 48 (1990), 359-375.*Amalgamations of lattice ordered groups*(with W. B. Powell), Lattice-Ordered Groups (A.M.W. Glass and W.C. Holland, Editors), D. Reidel, Dordrecht, 1989, 308-327.*Free products in varieties of lattice-ordered groups*(with W. B. Powell), Lattice-Ordered Groups (A.M.W. Glass and W.C. Holland, Editors), D. Reidel, Dordrecht, 1989, 278-307.*Sets of disjoint elements in free products of lattice ordered groups*(with W. B. Powell), Proc. Amer. Math. Soc. 104 (1988), 1014-1020.*Disjoint sets in free lattice ordered modules*(with W. B. Powell), Houston J. of Math. 15 (1989), 417-424.*The failure of the amalgamation property for varieties of representable l-groups*(with W. B. Powell), Math. Proc. Camb. Phil. Soc. 106 (1989), 439-443.*Covers of the variety of abelian l-groups*(with W. B. Powell), Comm. Alg. 17 (1989), 2461-2468.*Cofinality in universal algebra*(with M. Gould and A. Morel), Proceedings of the International Symposium on Ordered Algebraic Structures, Marseilles, 1984, 303-311.*Cofinality of algebras*(with M. Gould and A. Morel), Algebra Universalis 22 (1986), 253-278.*Meet-irreducible varieties of lattice ordered groups*(with W. B. Powell), Algebra Universalis 20 (1985), 262-263.*Globals of completely regular periodic semigroups*(with M. Gould and J. A. Iskra), Semigroup Forum 29 (1984), 365-374.*Globally determined lattices and semilattices*(with M. Gould and J. A. Iskra), Algebra Universalis 19 (1984), 137-141.*Amalgamations of lattice-ordered groups*(with W. B. Powell), in Ordered Algebraic Structures, Marcel Dekker (W. B. Powell and C. Tsinakis, editors), Lecture Notes in Pure and Applied Math., No. 99, Marcel Dekker, 1985, 171-178.*Free products of lattice ordered groups*(with W. B. Powell), Algebra Universalis 18 (1984), 178-198.*Projectable and strongly projectable lattice ordered groups,*Algebra Universalis 20 (1985), 57-76.*Disjointness conditions for free products of l-groups*(with W. B. Powell), Arch. Math. 46 (1986), 491-498.*Free products of abelian l-groups are cardinally indecomposable*(with W. B. Powell), Proc. Amer. Math. Soc. 86 (1982), 385-390.*The distributive lattice free product as a sublattice of the abelian l-group free product*(with W. B. Powell), J. Austral. Math. Soc. (Series A) 34 (1983), 92-100.*Free products in the class of abelian l-groups*(with W. B. Powell), Pacific J. Math. 104 (1983), 429-441.*On recovering a bounded distributive lattice from its endomorphism monoid*, (with R. McKenzie), Houston J. Math. 7(1981), 525-529.*Brouwerian semilattices determined by their endomorphism semigroups*, Houston J. Math. 5 (1979), 427-436.*Relative pseudo-complements, join-extensions and meet-retractions*(with J. Schmidt), Math. Z. 157 (1977), 271-284.

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