Peter Jipsen

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Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices have been studied in several branches of mathematics, including the areas of lattice-ordered groups, ideal lattices of rings, linear logic and(More)
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(More)
Approved: Date: ACKNOWLEDGEMENTS I wish to express my deepest gratitude to Bjarni Jónsson for all his advice, encouragement and patience. He directed me to this area of research and posed many interesting problems, some of which ultimately lead to this dissertation. His love and concern for mathematics are inspiring and will remain with me in the years to(More)
The poset product construction is used to derive embedding theorems for several classes of generalized basic logic algebras (GBL-algebras). In particular it is shown that every n-potent GBL-algebra is embedded in a poset product of finite n-potent MV-chains, and every normal GBL-algebra is embedded in a poset product of totally ordered GMV-algebras.(More)