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  1.  40
    Residuated Lattices: An Algebraic Glimpse at Substructural Logics.Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono - 2007 - Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
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  2.  42
    Algebraic Aspects of Cut Elimination.Francesco Belardinelli, Peter Jipsen & Hiroakira Ono - 2004 - Studia Logica 77 (2):209 - 240.
    We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. (...)
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  3.  28
    From Semirings to Residuated Kleene Lattices.Peter Jipsen - 2004 - Studia Logica 76 (2):291 - 303.
    We consider various classes of algebras obtained by expanding idempotent semirings with meet, residuals and Kleene-*. An investigation of congruence properties (e-permutability, e-regularity, congruence distributivity) is followed by a section on algebraic Gentzen systems for proving inequalities in idempotent semirings, in residuated lattices, and in (residuated) Kleene lattices (with cut). Finally we define (one-sorted) residuated Kleene lattices with tests to complement two-sorted Kleene algebras with tests.
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  4.  19
    Preface.Nikolaos Galatos, Peter Jipsen & Hiroakira Ono - 2012 - Studia Logica 100 (6):1059-1062.
  5.  10
    Generalizations of Boolean Products for Lattice-Ordered Algebras.Peter Jipsen - 2010 - Annals of Pure and Applied Logic 161 (2):228-234.
    It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we show that FLw-algebras decompose as a poset product over any finite set of join irreducible strongly central elements, and that bounded n-potent GBL-algebras are represented (...)
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  6.  21
    Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic.Elena Aladova, Pablo Barceló, Johan van Benthem, Gerald Berger, Katrin M. Dannert, Neil Dewar, Răzvan Diaconescu, Ivo Düntsch, Wojciech Dzik, M. Eyad Kurd-Misto, Giambattista Formica, Michèle Friend, Robert Goldblatt, Georg Gottlob, Erich Grädel, Robin Hirsch, Ian Hodkinson, Marcel Jackson, Peter Jipsen, Roger D. Maddux, J. B. Manchak, Ewa Orłowska, Andreas Pieris, Boris Plotkin, Tatjana Plotkin, Vaughan R. Pratt, Ian Pratt-Hartmann, Tarek Sayed Ahmed, James Owen Weatherall, Dag Westerståhl, James Wimberley, Krzysztof Wójtowicz & Christian Wüthrich (eds.) - 2021 - Springer Verlag.
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  7.  15
    On Tarski’s Axiomatic Foundations of the Calculus of Relations.Hajnal Andréka, Steven Givant, Peter Jipsen & István Németi - 2017 - Journal of Symbolic Logic 82 (3):966-994.
    It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, (...)
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  8.  5
    Partition Complete Boolean Algebras and Almost Compact Cardinals.Peter Jipsen & Henry Rose - 1999 - Mathematical Logic Quarterly 45 (2):241-255.
    For an infinite cardinal K a stronger version of K-distributivity for Boolean algebras, called k-partition completeness, is defined and investigated . It is shown that every k-partition complete Boolean algebra is K-weakly representable, and for strongly inaccessible K these concepts coincide. For regular K ≥ u, it is proved that an atomless K-partition complete Boolean algebra is an updirected union of basic K-tree algebras. Using K-partition completeness, the concept of γ-almost compactness is introduced for γ ≥ K. For strongly inaccessible (...)
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