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  1. Nikolaos Galatos, Peter Jipsen & Hiroakira Ono (2012). Preface. Studia Logica 100 (6):1059-1062.
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  2. Peter Jipsen (2009). Generalizations of Boolean Products for Lattice-Ordered Algebras. Annals of Pure and Applied Logic 161 (2):228-234.
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  3. Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono (2007). Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
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  4. Francesco Belardinelli, Peter Jipsen & Hiroakira Ono (2004). Algebraic Aspects of Cut Elimination. 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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  5. Peter Jipsen (2004). From Semirings to Residuated Kleene Lattices. 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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  6. Peter Jipsen & Henry Rose (1999). Partition Complete Boolean Algebras and Almost Compact Cardinals. Mathematical Logic Quarterly 45 (2):241-255.
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