College of Arts and Science Vanderbilt University

Constantine Tsinakis' Web Site

Bibliography

Fields of Interest

Algebra and Logic

Edited Volumes
  • Order, Algebra, and Logic, Special Issue of the Journal of Logic and Computation, to appear (edited with G. Metcalfe).
  • Ordered Algebraic Structures, Lecture Notes in Pure and Applied Math., No. 99, Marcel Dekker, 1985 (edited with W. B. Powell).
  • Modern Algebra and Its Applications, Theoretical Computer Science, Volume 249 (Number 1), 2000 (edited with K. Keimel and M. Mislove).
Articles
  • The Hulls of semi-linear GMV algebras (with José Gil-Férez, Antonio Ledda, and Francesco Paoli), in preparation.
  • The failure of the amalgamation property for semilinear varieties of ordered algebras (with José Gil-Férez, Antonio Ledda, and Francesco Paoli), in preparation.
  • The finite embeddability property for algebras of logic (with Simone Bova and Luca Spada), in preparation.
  • Lattice-theoretic properties of algebras of logic (with Antonio Ledda and Francesco Paoli), submitted for publication.
  • Semi-linear varieties of lattice-ordered algebras (with Antonio Ledda and Francesco Paoli), submitted for publication.
  • Amalgamation and interpolation in ordered algebras (with George Metcalfe and Franco Montagna), submitted for publication.
  • On Birkhoff’s “common abstraction" problem (with Francesco Paoli), to appear in Studia Logica.
  • 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.