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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Residuated frames with applications to decidability
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by Nikolaos Galatos and Peter Jipsen PDF
Trans. Amer. Math. Soc. 365 (2013), 1219-1249 Request permission


Residuated frames provide relational semantics for substructural logics and are a natural generalization of Kripke frames in intuitionistic and modal logic, and of phase spaces in linear logic. We explore the connection between Gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut-elimination, the finite model property and the finite embeddability property, which imply the decidability of the equational/universal theories of the associated residuated lattice-ordered groupoids. In particular these techniques allow us to prove that the variety of involutive FL-algebras and several related varieties have the finite model property.
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Additional Information
  • Nikolaos Galatos
  • Affiliation: Department of Mathematics, University of Denver, 2360 S. Gaylord Street, Denver, Colorado 80208
  • Email:
  • Peter Jipsen
  • Affiliation: Mathematics and CS, Faculty of Mathematics, School of Computer Science, Chapman University, One University Drive, Orange, California 92866
  • Email:
  • Received by editor(s): August 29, 2008
  • Received by editor(s) in revised form: February 22, 2011
  • Published electronically: October 31, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 1219-1249
  • MSC (2010): Primary 06F05; Secondary 08B15, 03B47, 03G10, 03F05
  • DOI:
  • MathSciNet review: 3003263