Downloadable 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 [pdf file] (with Antonio Ledda and Francesco Paoli), submitted for publication.
  • Join-completions of ordered algebras [pdf file] (with José Gil-Férez, Luca Spada and Hongjun Zhou), submitted for publication.
  • Recognizability in residuated lattices [pdf file] (with José Gil-Férez), to appear in Studia Logica.
  • Uniform interpolation and compact congruences [pdf file] (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 [pdf file] (with José Gil-Férez and Antonio Ledda), J. Algebra 483 (2017), 429-474.
  • Density revisited [pdf file] (with George Metcalfe), Soft Computing 21(1) (2017), 175-188.
  • Projectable l-groups and algebras of logic: categorical and algebraic connections [pdf file] (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 [pdf file] (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 [pdf file] (with José Gil-Férez and Antonio Ledda), Math Slovaca 65(4) (2015), 817-828.
  • Free objects and free extensions in the category of frames [pdf file], Math Slovaca 65(2) (2015), 1-8.
  • Semi-linear varieties of lattice-ordered algebras [pdf file] (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 [pdf file] (with Antonio Ledda and Francesco Paoli), Journal of Pure and Applied Algebra 218 (10) (2014), 1932-1952.
  • Amalgamation and interpolation in ordered algebras [pdf file] (with George Metcalfe and Franco Montagna), J. Algebra 402 (2014), 21-82.
  • On Birkhoff’s “common abstraction” problem [pdf file] (with Francesco Paoli), Studia Logica 100(6) (2012), 1079-1105.
  • Ordered groups with a conucleus  [pdf file] (with Franco Montagna), Journal of Pure and Applied Algebra 214 (1) (2010), 71-88.
  • Ordered algebras and logic [pdf file] (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.
  • Consequence relations: an order-theoretic and catagorical perspective [pdf file] (with Nikolaos Galatos), J. Symbolic Logic 74 (3) (2009), 780-810.
  • Ordinal decompositions for preordered root systems [pdf file] (with James Hart), Annals of Pure and Applied Logic 161 (2) (2009), 203-211.
  • The duality between algebraic posets and bialgebraic frames: a lattice theoretic  perspective [pdf file]  (with James Hart), Revista de la Unión Matemática Argentina 49 (1) (2008), 83-98.
  • Godel incompleteness in AF C*-algebras [pdf file] (with Daniele Mundici), Forum Math 20 (6) (2008), 1071–1084.
  • Perfect GMV-algebras [pdf file] (with Antonio Di Nola and Anatolij Dvurecenskij), Communications in Algebra 36 (4) (2008), 1221-1249.
  • A concrete realization of the Hoare powerdomain [pdf file] (with James B. Hart), Soft Computing 11 (11) (2007), 1059-1063.
  • Minimal varieties of involutive residuated lattices [pdf file] (with Annika Wille), Studia Logica 83 (2006), 401-417.
  • Generalized MV-algebras [pdf file] (with N. Galatos), J. Algebra 283(1) (2005), 254-291.
  • Products of classes of residuated structures [pdf file](with Bjarni Jonnson), Studia Logica 77 (2004), 267-292.
  • Order algebras as models of linear logic [pdf file](with Han Zhang), Studia Logica 76 (2004), 195-219.
  • Cancellative residuated lattices [pdf file] (with P. Bahls, J. Cole, N. Galatos and Peter Jipsen), Algebra Universal. 50 (1), (2003), 83-106.
  • A survey of residuated lattices [pdf file] (with P. Jipsen), Ordered Algebraic Structures (J. Martinez, editor), Kluwer Academic Publishers, Dordrecht, 2002, 19-56.
  • The Structure of residuated lattices [pdf file] (with K. Blount), Internat. J. Algebra Comput. 13(4) (2003), 437–461.
  • The structure of commutative residuated lattices [pdf file] (with J. Hart and Lori Rafter), Internat. J. Algebra Comput. 12 (2002), no. 4, 509-524.

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Contact Information

Constantine Tsinakis
Professor of Mathematics

Office: Stevenson Center 1406
Phone: 615-343-5629
Fax: 615-343-8702

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