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.